QUANTUM MECHANICS AND ATOMIC STRUCTURE
description
Transcript of QUANTUM MECHANICS AND ATOMIC STRUCTURE
General Chemistry I 1
QUANTUM MECHANICSAND ATOMIC STRUCTURE
51 The Hydrogen Atom
52 Shell Model for Many-Electron Atoms
53 Aufbau Principle and Electron Configurations
54 Shells and the Periodic Table Photoelectron Spectroscopy
55 Periodic Properties and Electronic Structure
5CHAPTER
General Chemistry I
General Chemistry I 2
Colors ofFireworks
from atomic emission
red from Sr
orange from Ca
yellow from Nayellow from Na
green from Ba
blue from Cu
General Chemistry I 3
51 THE HYDROGEN ATOM
- The hydrogen atom is the simplest example of a one-electron atom or ion (ie H He+ Li2+ hellip)
- For solution of the Schroumldinger equation
spherical coordinates r
Cartesian coordinates x y z
to express angular orientation
General Chemistry I 4
Energy Levels
For a hydrogen atom V(r) = Coulomb potential energy
Solutions of the Schroumldinger equation
1 rydberg = 218times10-18 J
Principal quantum number n indexes the individual energy levels
E = En =Z2e4me
8 02n2h2
_ n = 1 2 3
General Chemistry I 5
Coordinate Systems
2 2 2 2
2 2 2 2( ) ( ) ( )
8
hV x y z x y z E x y z
m x y z
2 2 2 2 2
2 2 2 2 2 2 2( ) ( )
8 ( )
h ex y z E x y z
m x y z x y z
- Cartesian Coordinates
- Spherical Polar Coordinates (SPC)2 2 2
22 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
Spherical polar coordinates (r θ Ф) vs Cartesian coordinates (x y z)
V(x y z) ndash can be expressed in various coordinate systems
For Coulomb potential V convenient to express
in SPC (V = -e2r) Cartesian V = -e2[x2 + y2 +z2]12
General Chemistry I 6
Quantization of the Angular Momentum
any integral value from 0 to n-1
value of l 0 1 2 3
orbital type s p d f orbitals
General Chemistry I 7
For every value of n n2 sets of quantum numbers
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 2
Colors ofFireworks
from atomic emission
red from Sr
orange from Ca
yellow from Nayellow from Na
green from Ba
blue from Cu
General Chemistry I 3
51 THE HYDROGEN ATOM
- The hydrogen atom is the simplest example of a one-electron atom or ion (ie H He+ Li2+ hellip)
- For solution of the Schroumldinger equation
spherical coordinates r
Cartesian coordinates x y z
to express angular orientation
General Chemistry I 4
Energy Levels
For a hydrogen atom V(r) = Coulomb potential energy
Solutions of the Schroumldinger equation
1 rydberg = 218times10-18 J
Principal quantum number n indexes the individual energy levels
E = En =Z2e4me
8 02n2h2
_ n = 1 2 3
General Chemistry I 5
Coordinate Systems
2 2 2 2
2 2 2 2( ) ( ) ( )
8
hV x y z x y z E x y z
m x y z
2 2 2 2 2
2 2 2 2 2 2 2( ) ( )
8 ( )
h ex y z E x y z
m x y z x y z
- Cartesian Coordinates
- Spherical Polar Coordinates (SPC)2 2 2
22 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
Spherical polar coordinates (r θ Ф) vs Cartesian coordinates (x y z)
V(x y z) ndash can be expressed in various coordinate systems
For Coulomb potential V convenient to express
in SPC (V = -e2r) Cartesian V = -e2[x2 + y2 +z2]12
General Chemistry I 6
Quantization of the Angular Momentum
any integral value from 0 to n-1
value of l 0 1 2 3
orbital type s p d f orbitals
General Chemistry I 7
For every value of n n2 sets of quantum numbers
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 3
51 THE HYDROGEN ATOM
- The hydrogen atom is the simplest example of a one-electron atom or ion (ie H He+ Li2+ hellip)
- For solution of the Schroumldinger equation
spherical coordinates r
Cartesian coordinates x y z
to express angular orientation
General Chemistry I 4
Energy Levels
For a hydrogen atom V(r) = Coulomb potential energy
Solutions of the Schroumldinger equation
1 rydberg = 218times10-18 J
Principal quantum number n indexes the individual energy levels
E = En =Z2e4me
8 02n2h2
_ n = 1 2 3
General Chemistry I 5
Coordinate Systems
2 2 2 2
2 2 2 2( ) ( ) ( )
8
hV x y z x y z E x y z
m x y z
2 2 2 2 2
2 2 2 2 2 2 2( ) ( )
8 ( )
h ex y z E x y z
m x y z x y z
- Cartesian Coordinates
- Spherical Polar Coordinates (SPC)2 2 2
22 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
Spherical polar coordinates (r θ Ф) vs Cartesian coordinates (x y z)
V(x y z) ndash can be expressed in various coordinate systems
For Coulomb potential V convenient to express
in SPC (V = -e2r) Cartesian V = -e2[x2 + y2 +z2]12
General Chemistry I 6
Quantization of the Angular Momentum
any integral value from 0 to n-1
value of l 0 1 2 3
orbital type s p d f orbitals
General Chemistry I 7
For every value of n n2 sets of quantum numbers
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 4
Energy Levels
For a hydrogen atom V(r) = Coulomb potential energy
Solutions of the Schroumldinger equation
1 rydberg = 218times10-18 J
Principal quantum number n indexes the individual energy levels
E = En =Z2e4me
8 02n2h2
_ n = 1 2 3
General Chemistry I 5
Coordinate Systems
2 2 2 2
2 2 2 2( ) ( ) ( )
8
hV x y z x y z E x y z
m x y z
2 2 2 2 2
2 2 2 2 2 2 2( ) ( )
8 ( )
h ex y z E x y z
m x y z x y z
- Cartesian Coordinates
- Spherical Polar Coordinates (SPC)2 2 2
22 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
Spherical polar coordinates (r θ Ф) vs Cartesian coordinates (x y z)
V(x y z) ndash can be expressed in various coordinate systems
For Coulomb potential V convenient to express
in SPC (V = -e2r) Cartesian V = -e2[x2 + y2 +z2]12
General Chemistry I 6
Quantization of the Angular Momentum
any integral value from 0 to n-1
value of l 0 1 2 3
orbital type s p d f orbitals
General Chemistry I 7
For every value of n n2 sets of quantum numbers
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 5
Coordinate Systems
2 2 2 2
2 2 2 2( ) ( ) ( )
8
hV x y z x y z E x y z
m x y z
2 2 2 2 2
2 2 2 2 2 2 2( ) ( )
8 ( )
h ex y z E x y z
m x y z x y z
- Cartesian Coordinates
- Spherical Polar Coordinates (SPC)2 2 2
22 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
Spherical polar coordinates (r θ Ф) vs Cartesian coordinates (x y z)
V(x y z) ndash can be expressed in various coordinate systems
For Coulomb potential V convenient to express
in SPC (V = -e2r) Cartesian V = -e2[x2 + y2 +z2]12
General Chemistry I 6
Quantization of the Angular Momentum
any integral value from 0 to n-1
value of l 0 1 2 3
orbital type s p d f orbitals
General Chemistry I 7
For every value of n n2 sets of quantum numbers
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 6
Quantization of the Angular Momentum
any integral value from 0 to n-1
value of l 0 1 2 3
orbital type s p d f orbitals
General Chemistry I 7
For every value of n n2 sets of quantum numbers
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 7
For every value of n n2 sets of quantum numbers
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 8
These sets of state are said to be degenerate
Energy level diagram for the H atom
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 9
Boundary Conditions
Boundary Conditions yield quantum numbers
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 10
Wave Functions
radial part angular part spherical harmonics
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 11
( ) ( ) ( )r R r Y
- Spherical Polar Coordinates and the Wave Function
2 2 22
2 2 2 2 2 2
1 1 1sin ( ) ( )
8 sin sin
h er x y z E x y z
m r r r r r r
2 2 22
2 2 2 2 2 2
1 1 1( ) sin ( ) 0
8 sin sin
h er E x y z x y z
m r r r r r r
2 2 2 22 2
2 2 2
1 1( ) sin ( ) 0
8 sin sin
h e rr Er x y z x y z
m r r r
Depends only on r Depends only on
- Schroumldinger wave function
rarr factored into radial (R) and angular (Y) functions
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 12
Orbitals
EXAMPLE 51
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 13
Specification of the Wave Functions Orbitals Schroumldingerrsquos Wave Function
ie) n = 3 (only one orbit in the Bohr- de Broglie model)
32 (nine) different ways the electron can vibrate to form a standing wave rarr 9 degenerate quantum states
Orbitals
replacement of Bohrrsquos orbit for 3D Schroumldingerrsquos wave function
- Radial part Rnℓ(r)
Laguerre polynomial (rn-1) x e-r(na0
)
- Angular part Yℓm(θФ)
Legendre function (sin θ amp cos θ) x eimФ
a0 larr Bohrrsquos radius
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 14
SphericalSymmetryno angularnodes
1 angularnode
2 angular nodes
n = 1
n = 2
n = 3
No radial node
1 radial node
2 radial nodes
No radial node
1 radial node
n = 3
n = 2
No radial noden = 3
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 15
Sizes and Shapes of Orbitals
Graphical representations of the orbitals
1) Slicing up 3D space into various 2D and 1D regions and examining the value of wave function at each point
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 16
2) Looking only at the radial behavior (ldquovertical slicerdquo)
R100(r)
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 17
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 18
s orbitals
s orbital
constant Y
All s orbitals arespherically symmetric
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 19
a function of r only
spherically symmetrical
exponentially decaying
no nodes
- 1s (n = 1 ℓ = 0 m = 0) R10(r) and Y00(θФ)
- 2s (n = 2 ℓ = 0 m = 0) R20(r) and Y00(θФ)
zero at r = 2a0 = 106Aring
nodal sphere or radial node
[rlt2ao Ψgt0 positive] [rgt2ao Ψlt0
negative]
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 20
isosurface1s2s
3s
wave functionplot
radialprobability
density(or function)
plot
A surface of pointswith the same valueof wave functions
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 21
Radial Distribution Functions RDFs
Prob(r) = r2[R(r)]2
Ψ2 x 4πr2 dr
2 2 2
0 0
2 22 2
2 22
222
22
sin
4 4 ( ) ( )
4 ( ) ( )
4 ( ) 1 2
( )
r d d
r r R r Y
r R r Y
r R r
r R r
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 22
Boundary Surfaces
- No clear boundary of an atom
- Defining the size of atom as the extent of a ldquoballoon skinrdquo inside which 90 of the probability density of the electron is contained
1s 141 Aring 2s 483 Aring 3s 1029 Aring
An ns orbital has n-1 radial nodes
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 23
p Orbitals
2p0 orbital R21 Y10 (n = 2 ℓ =1 m = 0)
middot Ф = 0 rarr cylindrical symmetry about the z-axis
middot R21(r) rarr ra0 no radial nodes except at the origin
middot cos θ rarr angular node at θ = 90o x-y nodal plane
middot r cos θ rarr z-axis 2p0 rarr labeled as 2pz
2
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 24
2p+1 and 2p-1 orbitals R21Y11 R21Y1-1 (n = 2 ℓ = 1 m = plusmn1)
middot Y11(θФ) rarr eplusmniФ = cosФ plusmn i sinФ larr Eulerrsquos formula was used
middot taking linear combinations of these gave two real orbitals
called 2px and 2py
- px and py differ from pz only in the angular
factors (orientations)
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 25
2p 3p
Wave function and RDF plots for 2p and 3p orbitals
r2Rnl2
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 26
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 27
d Orbitals
d-orbitals
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 28
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 29
Orbital Shapes and Sizes General Notes
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 30
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 31
Stern-Gerlach Experiment experimental evidence for the existence of electron spin
Stern and Gerlach (1926) Ground state Na atoms were passed through a
strong inhomogeneous magnetic field
All spin magnetisms in inner orbitals
rarr cancelled except an electron in 3s
orbital
Y (θФ)(3s) rarr no rotation
The intrinsic magnetism of the 3s electron
rarr only possible to respond to the external
field
3s electrons rarr line up with their north
poles either along or against the main
north pole of the magnet
The lack of a ldquostraight-throughrdquo beam
with the magnet rarr clear evidence of two-
valued electronrsquos magnetism
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 32
Electron Spin
- An electron has two spin states as uarr(up) and darr(down) or a and b
ms spin magnetic quantum number
- the values of ms only +12 and -12
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 33
52 SHELL MODEL FOR MANY-ELECTRON ATOMS
- In many-electron atoms Coulomb potential energy equals the sum of nucleus-electron attractions and electron-electron repulsions
- No exact solutions of Schroumldinger equation
- In a helium atom
r1 = the distance of electron 1 from the nucleus
r2 = the distance of electron 2 from the nucleus
r12 = the distance between the two electrons
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 34
Interparticle distance in He
Screening of one electron by another
r1equiv (r1θ1Ф1)
r2equiv (r2θ2Ф2)
r12 equiv r 1 ndash r2
interelectron distance
Repulsion between electronsThis new cross-term makes the Schrodinger equation impossible to solve exactly and causes the Bohr model to fail for He and other atoms
11 1 1 2 2 2 2( ) ( )r r r r
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 35
Hartree Orbitals
Self-consistent field (SCF) orbital approximation method by Hartree Fock Slater and others
- Building up an effective nuclear charge Zeffe
1 11 1 1 2 2 2 2 2( ) ( ) ( ) ( )a br r r r r r
- all electrons were treated as independent meaning that we
neglect the repulsion term
ie) for He
Zeff(He) = 16875 lt 2
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 36
Three simplifying assumptions by Hartree
The wave function becomes a product of these one-electron orbitals
3 The effective field is spherically symmetric that is it has no angular dependence
The equations for the unknown effective field and the unknownone-electron orbitals must be solved by iteration until a self-consistent solution is obtained
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 37
1 0 2 0
1 0 2 0
1 0 2
3 2 3 2 0 0
1 12 2
3 2 3 2
0 0
3
30
1 1( ) ( ) ( )
1 1eff eff
eff eff
Zr a Zr aa b
Z r a Z r a
eff eff
Z r a Z r aeff
a ar r r r e e
Z Z
a ae e
Z Z
Ze e
a
0
Eg for the ground state of He
1s orbital1s orbital
1s2
occupancy
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 38
The ground state of Ar Z = 18
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 39
sum of the radial probability density functionsof all the occupied orbitals
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 40
Shielding Effects
- Energy-level diagrams for many-electron atoms
1) The degeneracy of the p d and f orbitals is removed due to the difference of Zeff from the Coulomb field
2) Energy values are distinctly shifted from the values of corresponding H orbitals due to the strong attraction by nuclei with Z gt 1
- Each electron attracted by the nucleus and repelled by the other electrons
rarr shielded from the full nuclear attraction by the other electrons
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 41
- effective nuclear charge Zeff e lt Ze
- Hartree orbital energy (rydbergs)
Eg For Ar (Z =18) Zeff(1) ~ 16 Zeff(2) ~ 8 Zeff(3) ~ 25
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 42
Energy level diagram for many-electron atoms
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 43
Penetration
s-electron ndash very close to the nucleushighly penetrates through the inner shell
p-electron ndash penetrates less than an s-orbitaleffectively shielded from the nucleus
In a many-electron atom because of the effects ofpenetration and shielding the order of energiesof orbitals in a given shell is s lt p lt d lt f
Zeff(s) gt Zeff(p) gt Zeff(d) gt Zeff(f)
Order of orbital shielding (for fixed value of n)
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 4444
The Building-up (Aufbau) Principle is a set of rules that allows us to construct ground state electron configurationsof the elements
1 Assume electrons lsquooccupyrsquo orbitals in such a way as to minimize the total energy (lowest energy first)
2 Assume a maximum of two electrons can lsquooccupyrsquo an orbital and these must have opposite spins (Paulirsquos Exclusion Principle no two electrons in an atom can have the same set of quantum numbers)
3 Assume electrons occupy unoccupied degenerate subshell orbitals first and with parallel spins (Hundrsquos rule)
In building-up electron configurations in order of energy subshell energy overlap must be taken into account (see later)
53 AUFBAU PRINCIPLE AND ELECTRON CONFIGURATIONS
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 45
H 1s1
He 1s2
Li 1s22s1 or [He]2s1
Electron configuration of an atom is a list of all its occupied orbitals with the numbers of electrons that each one contains
Electron configurations of first ten elements (H to Ne)
Standard notation Box and arrow notation(showing electron spins)
Core electrons
Valence electron
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 46
Be 1s22s2 or [He]2s2
B 1s22s22p1 or [He]2s22p1
C 1s22s22p2 or [He]2s22p2
parallel spinsby Hundrsquos rulerarr 1s22s22px
12py1
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 47
- Elements in Period 2 (from Li to Ne) the valence shell with n = 2
- p-block elements N to Ne filling of p orbitals
s-block elements H to Be filling of s orbitals
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 48
Magnetic properties as a test of electronic configurations
- paramagnetic a substance attracted into a magnetic fieldwith one or more unpaired electrons
- diamagnetic a substance pushed out of a magnetic fieldwith all electrons paired
Examples paramagnetic H Li B Cdiamagnetic He Be
C
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 49
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 50
n = 3 Na [He]2s22p63s1 or [Ne]3s1 to Ar [Ne]3s23p6
n = 4 from Sc (scandium Z = 21) to Zn (zinc Z = 30) the next 10 electrons enter the 3d-orbitals (d-block elements)
The (n+l) rule Order of filling subshells in neutral atoms is
determined by filling those with the lowest
values of (n+l) first Subshells in a group with
the same value of (n+l) are filled in order
of increasing n due to orbital screening
order 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt hellip
n = 5 5s-electrons followed by the 4d- electrons n = 6 Ce (cerium [Xe]4f15d16s2)
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 5151
Alternative Pictorial Representation of Orbital Energy Order
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 52
Anomalous Configurations
Exceptions to the Aufbau principle
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 53
Filling of electron subshells in relationto the periodic table
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 54
All atoms in a given period have the same type of core with the same n
All atoms in a given group have analogous valence electron configurationsthat differ only in the value of n
Period 2
Period 3
Period 4
Group 1IA Group 18VIII
Period 5
Period 6
Period 7
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 55
54 SHELLS AND THE PERIODIC TABLE PHOTOELECTRON SPECTROSCOPY
A shell is defined precisely as a set of orbitals that have the same principal quantum number
The photoelectron spectroscopy (PES) principledetermining the energy level of each orbital by measuring theionization energy required to remove each electron from the atom
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 56
Basic design of a PEspectrometer
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 57
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 58
- Koopmansrsquo approximation
- with the frozen orbital approximation
Eg for Ne with 1s2 2s2 2p6
the orbital energies are the samein the ion despite the loss of anelectron
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 59
528 Photoelectron spectroscopic studies of silicon atoms excited by X-rays of wavelength9890 x 10-10 m show four peaks in which the electrons have speeds (all x 107 ms)of (1) 2097 (2) 2093 (3) 2014 and (4) 1971(a) Calculate the ionization energy of the electrons corresponding to each peak(b) Assign each peak to an orbital of the silicon atom1eV = 16022 x 10-19 J c = 299792 x 108 ms h = 662607 x 10-34 J sme = 910938 x 10-31 kg
Solutions
(a) E(X-rays) = h = hc =(662607 x 10-34 J s)(299792 x 108 ms)
9890 x 10-10 m
= 20085 x 10-16 J =1 eV
16022 x 10-19 J(20085 x 10-16 J)
= 12536 eV
Using the PES equation IE = h - KE = h - 12mev2
IE(1) = 12536 eV _ (910938 x 10-31 kg)(2097 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 35 eV
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 60
IE(2) =12536 eV _ (910938 x 10-31 kg)(2093 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 83 eV
IE(3) =12536 eV _ (910938 x 10-31 kg)(2014 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1005 eV
IE(4) =12536 eV _ (910938 x 10-31 kg)(1971 x 107 ms)2
2
1 eV
16022 x 10-19 J
= 1492 eV
(b) The ground-state electron configuration of silicon is 1s22s22p63s23p2 Peak 1corresponds to removal of siliconrsquos 3p electrons which are its least tightly boundelectronsPeaks 2 3 and 4 correspond to removal of Sirsquos 3s 2p and 2s electronsrespectively The 1s electron does not give a peak It is probably at an energylower than ndash12536 eV and inaccessible with the X-radiation used in thisexperiment
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 61
(Fig 525)Energies of atomicsubshellsdeterminedby PES
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 62
55 PERIODIC PROPERTIES AND ELECTRONIC STRUCTURE
Atomic radius defined as half the distance between the centers ofneighboring atoms
- r decreases from left to right across a period (effective nuclear charge increases)
- r increases from top to bottom down a group (change in n and size of valence shell)
General trends
Ionic radius its share of the distance between neighboring ions in an ionic solid
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 63
- The rate of increase changes considerably
ie Li+ Na+ to K+
substantial change
to Rb+ Cs+
small change due to filling d-orbitals
Lanthanide contraction
filling of the 4f orbitals(poor shielders) radii of 3rd row D-block elementssimilar to those of 2nd row
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 64
Molar volumes (cm3 mol-1) of atoms in the solid phase
= size of the atoms + geometry of the bonding
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 65
Periodic Trends in Ionization Energies
From He to Li a large reduction in IE1
2s e- further than 1s e- and 2s e- seesa net +1 charge
From Be to B slight reduction in IE1
fifth e- in a higher energy 2p orbital
From N to O slight reduction in IE1
2 e- in the same 2p orbital leading togreater repulsion
From left to right generally increase in IE1 due to the increase of Zeff
From top to bottom generally decrease in IE1 due to the increase of n
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 66
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 67
Electron Affinity
(kJ mol-1)
- The periodic trends in EA parallel those in IE1 with one unit lower shifteg F to F- large EA because of its closed-shell configuration
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56
General Chemistry I 68
10 Problem Sets
For Chapter 5
6 18 22 28 32 38 44 46 48 56