Atomic Structure & Periodicity

Electromagnetic Radiation

wavelength and frequency are inversely related

= c/

Photosynthesis uses light with a frequencyof 4.54 x 1014 s-1. What is the wavelength of this light?

4.54 x 1014s-1 = 3.0 x 108 ms-1/= 6.60 x 10-7 m

E = h

• Max Plank found that energy is not continuous, but occurs in discrete units called QUANTA

• h is Planck’s constant = 6.626 x 10-34 J s• gives energy PER PHOTON• It takes 382 kJ of energy to remove one

MOLE of electrons from gaseous Cs. What is the wavelength associated with this energy?

(382000 J/mol) x

(1mol/6.022 x1023) = 6.343 x 10-19 J

= 9.57 x 1014 s-1

= 3.13 x 10-7 m

• Einstein assigned the word PHOTON to mean a particle of light

• E = h and E = mc2 and = c/

• Therefore the mass of a photon can be calculated: m = h/c

If light has mass, does matter have wavelength?

DeBroglie equation: = h/mv

mass must be in kilograms

*velocity is in m/s

Sample Problem

Compare the wavelength of an electron (mass = 9.11 x 10-31 kg)

traveling at 1.0 x 107 m/s

to that of a ball (mass 0.10 kg)

traveling at 35 m/s.

electron

(6.626 x 10-34 Js)/(9.11 x 10-34 x 1.0 x107)

= 7.27 x 10-11 m

ball

(6.626 x 10-34 Js)/(0.10 x 35)

= 1.89 x 10-34 m

Light

Bohr Model

E = -2.178 x 10-18 J (z2/n2)

E = -2.178 x 10-18J (z2/nf2 – z2/ni

2)

Calculate the energy required to excite the hydrogen electron from n = 1 to n = 3.

-2.178 x 10-18 (1/9 -1/1)

= 1.936 x 10-18 J

Polyelectronic Atoms

Electron Correlation Problem

Electrons repel each other, so solving for energy becomes complicated because of the electron-electron repulsions

Effective Nuclear Charge

Zactual – (effect of electron repulsions)

The “effectiveness” of the nucleus is decreased by electron repulsions

What determines Zeff?ShieldingInner electrons repel each other and in so

doing, protect outer electrons from the pull of the nucleus

Penetration EffectAlthough 90% of the time an outer electron

is far from the nucleus, there is a chance it comes close to the nucleus. This ______

the effective nuclear charge.

Finding the value of Zeff

1) Determine the ionization energy from experiment.

2) E = -2.178 x 10-18 (Zeff2/nf

2 – Zeff2/ni

2)

3) solve for Zeff where nf is infinity

Note: E = (1310 kJ/mol) (Z2/n2)

Sample Problem

Calculate the effective nuclear charge on a 1s electron of a sodium atom.

(IE = 139000 kJ/mol)

139000 kJ/mol = (1310 kJ/mol) (Z2/12)

Z = +10.3

Now try…

Calculate the effective nuclear charge for a 3s electron in a sodium atom.

(IE = 495 kJ/mol)

495 kJ/mol = 1310 kJ/mol (Z2/32)

= +1.84

So the n = 1 electron was held by the nucleus 5.6 times more strongly than the n = 3 electron…

Quantum Mechanical ModelQuantum Mechanical Model

H = Ewave functions = orbitals

Probability Clouds

2 = probability of finding an electron

Aufbau Principle

As protons are added one by one to the nucleus to build up the element, electrons are similarly added to these orbitals.

Add to the lowest energy level first until it is full, then add to next energy level.

Order of Filling

Hund’s Rule

The lowest energy configuration for an atom has the maximum number of unpaired electrons.

(electrons will go into degenerate orbitals singly before doubling up)

Example: Oxygen 1s 2s 2p

Pauli Exclusion Principle

In a given atom, no two electrons can have the same set of four quantum numbers.

**a maximum of 2 electrons can occupy an orbital, **a maximum of 2 electrons can occupy an orbital, but they must have opposite spins**but they must have opposite spins**

Electrons that are in the same orbital would have the same n, l, ml values, but different ms values (opposite spins)

Valence Electrons

electrons in outermost (highest) energy level

Core Electrons

the inner electrons (all but the valence e-)

Quantum NumbersQuantum Numbers

Principle Quantum Number (n)

Relates size & energy of the orbital

big n = higher energy = big orbital

Angular Quantum Number (l)relates the shape of the orbital

0 = s 1 = p

2 = d 3 = f

complex

Magnetic Quantum Number (ml)

Relates the orientation of the orbital in space

Spin Quantum Number (ms)

either + ½ or – ½

Allowed Quantum Numbers

n = natural numbers

l = at least one less than n

ml = -l to +l

ms = + ½ or - ½

Which are NOT allowed?

n l ml ms

0 -1 0 01 0 0 + ½2 2 -2 - ½3 1 0 - ½7 3 -1 + ½

Atomic Radius• relates the size of an atom

• increases down and left

Periodic Trends

Can be explained by the following two facts!

1) As you move down a group on the periodic table…the number of energy levels increases.

2) As you move from left to right on the periodic table…the effective nuclear charge increases.

Ionization Energy

• energy required to remove an electron from a gaseous atom

(to n = infinity)

• Increases up and to the right • First IE is removing the outermost electron

• Second IE is removing the next farthest e- and so on

Periodic Trends

Can be explained by the following two facts!

1) As you move down a group on the periodic table…the number of energy levels increases.

2) As you move from left to right on the periodic table…the effective nuclear charge increases.

Ionic Radius

• cation is smaller than its parent atom

• anion is larger than its parent atom

• within the + ions OR within the – ions size increases left and down

Electron Affinity

• energy associated with adding an electron to a gaseous atom or ion

• generally increases up and right

Electronegativity

A measure of an atom’s ability to attract electrons from a bond.

Increases up and to the right.

What is the most electronegative element?

Noble gases do not bond, so by definition have no electronegativity.

So What?

1) As we move down, the outermost electrons are getting farther from the nucleus, so although the number of protons is increasing their effect is cancelled out by the increased electron repulsion (shielding)

So What?

2)As we move across there are more protons, but the number of energy levels remains constant. So the valence electrons of each element are about the same distance from the nucleus BUT the nucleus is getting “stronger.”