Quantum Mechanics & Electron Configuration

Chapter 5: Electrons in Atoms

Part 1: Models of the Atom

1897: Thompson Model (Plum Pudding)

1911: Rutherford Model – Small, dense, + charged nucleusElectrons orbit around

1913: Bohr Model

1926: Quantum Mechanical Model – Erwin Schrodinger & his math equations

Bohr Model (aka the versions you’ve learned before)

Electrons move around the nucleus in fixed spherical orbits with fixed energies Fixed energies = orbits / energy levels

Aka rungs of a ladder

Electrons can go to a higher or lower energy level Either gain or lose energy to move levels

Electrons CANNOT be between levels

Atomic Emission Spectra** When atoms absorb energy (i.e. electric current), they move to a higher energy level …

… these electrons emit light when they return back to a lower energy level

Emission spectra is unique for each element- The light emitted consists of only a mixture to specific

frequencies…

If you pass the light through a slit and then a prism, you can separate the resulting light into its frequencies (aka colors)

Barium

Light

Has properties of both: a Particle ( ____________) a Wave

Light Waves:Amplitude: crest of the wave (height from 0)Wavelength: distance between crests (λ)Frequency: # of waves per unit time (ν)

Units: Hertz (Hz) aka s-1

Math Time!!!

c = λνC = speed of light (constant) = 2.998 x 108 m/s

λ = Wavelength (m)

ν = Frequency (Hz or s-1)

More Math… The energy (E) of a photon is directly

proportional to its frequency. Higher freq = More EnergyLower Freq = Less Energy

E = h x v

E = energy (joules – J)H = Plank’s constant = 6.626E-34 J/sv = Frequency (Hz or s-1)

Example:

What is the energy of a quantum of light with a frequency of 7.39 x 1014 Hz?

Think about this… E = h x v c = λν

What would you do if you were asked to solve for the frequency of light if you are given a wavelength of 700nm?

What would you do if you were asked to find the energy of light if you are given a wavelength of 480nm?

Emission Spectra LabLook at the gas tubes and follow directions provided.

Continuous Spectrum v. Line Spectrum What did you observe in the Emission

Lab?

Light has Wave-Particle Duality (& so do electrons)

Particle & Wave-like Nature Depends on experiment / what we try to

observe

Throws a wrench in Bohr Model… New method of describing the motion of

subatomic particles= foundation of quantum mechanics = movement/organization of subatomic particles

The Quantum Mechanical Model

This is what we use today

Describes: LOCATION & ENERGY of electrons

Electrons do not have a direct orbit around nucleus Based on probability Electron clouds

Electrons do have energy levels

Hog Hilton Sample Problem Book 15 hogs into their rooms

6th floor ____ ____ ____ _____ _____6th floor ______5th floor ______ ______ ______4th floor ______3rd floor ______ ______ ______2nd floor ______1st floor ______

Hog Hilton Sample ProblemPlace 15 electrons into their spaces

3d_____ _____ _____ _____ ____4s _____3p ______ ______ ______3s ______2p ______ ______ ______2s ______1s ______

But…all of these electrons are not organized into hotel rooms, but ATOMIC ORBITALS

So, what exactly is an ATOMIC ORBITAL?

Atomic Orbital = region of space in which there is a high probability of finding an electron

They come in different SHAPES, SIZES & ENERGY LEVELS!!

These are described by Quantum Numbers…

Part 2Quantum Numbers

Get ready…here we go…

Quantum Numbers

Used to describe the location of electrons

Electrons in an atom CANNOT have the same quantum numbers

Unique for each electron Like an address

Principle Quantum Number (think…Energy Level)

n

Allowable values = 1, 2, 3 … n (positive, integer values)

Describes energy level

Position of the electron w/ respect to nucleus As n increases = further from nucleus

Angular Momentum Quantum Number (Azimuthal Quantum Number)(think…energy sublevel)Pay attention…this is where it starts to get complicated

l

Allowed values: 0, 1, 2, … (n-1)

Describes the sublevel SHAPE of the orbital

SHAPES: l = 0 = s orbital = spherical cloud l = 1 = p orbital = dumbbell cloud l = 2 = d orbital = clover cloud l = 3 = f orbital = … too complicated

Example If I had a principal quantum number of

2, what are my possible angular momentum quantum numbers?

n = 2

l =

Angular Momentum Quantum Number: Orbital Shapes

Magnetic Quantum Number (ml) Determines spatial orientation (x, y, z, plane)

Possible Values: - l to + l Examples: if it is a d orbital

d orbital:l = ml =

Example: p-orbitaln = 2l = ml =

This means, there are _______ p-orbitals and that they are in three directions (x, y, z axes):

What orbital corresponds to :n = 2l = 1ml = 0

Energy level =Sublevel = _____ - orbitalOrientation:Orbital:

Number of orbitals within an energy level: n2

Examples: How many orbitals are in energy level 2?n = l = ml =

Orbitals =

Each orbital holds 2 electrons:So, how many electrons can energy level 2 hold?

# Electrons = 2n2

Spin Quantum Number

ms

Describes the direction of the electrons spin within an orbital (remember, each orbital only holds 2 electrons)

Possible Values: ½ or -½ (spin up, spin down)

Think back to hogs…

Ahhh…it’s too much information…HELP!!!

Solution: STUDY and PRACTICE!!!

Quantum # Symbol Possible Values Description

Principle Quantum Number

n 1, 2, 3, etc Energy level

Angular Momentum

Quantum Number

l 0 … n-1 Sublevel & shape

Magnetic Quantum Number

ml -l … +l Spatial Orientation of orbital (x,y,z)

Spin Quantum Number

ms +½ or -½ Direction of Spin

Examples

1. n = 3 (what are the possible quantum numbers?)

2. What orbital corresponds to n = 4 & l = 2?

What orbital corresponds to n = 4 , l = 1, ml = -1

Energy Level = Sublevel = Orbital orientation = Orbital =

Re-iterate:Orbital How Many Types of

Orbitals (orientations)

How Many Electrons in Shape

s 1

p 3

d 5

f 7

Principle Quantum Number

(n)

Angular Momentum Quantum Number

(sublevels)(l)

Shapes of Sublevels

# electrons (2n2)

1

2

3

4

5

6

7

Principle Quantum Number

(n)

Angular Momentum

Quantum Number (sublevels)

(l)

Shapes of Sublevels

# electrons (2n2)

1 0 s 2

2 0, 1 s p 8

3 0, 1, 2 s p d 18

4 0, 1, 2, 3 s p d f 32

5 0, 1, 2, 3, 4 s p d f (g) 50

6 0, 1, 2, 3, 4, 5 s p d f (g h) 72

7 0, 1, 2, 3, 4, 5, 6 s p d f (g h i) 98

STOPDo You Have Any Questions?

PART 3 Rules of Electron Configuration

Aufbau Principle

Electrons enter orbitals of lowest energy first

Orbitals within a sublevel have equal energy(3px, 3py, 3pz)

Exceptions: Cr , Cu

Which hog rules is this?

Pauli Exclusion Principle An atomic orbital may only hold two

electrons

Electrons must have opposite spin

Clockwise or counterclockwise spin Denoted with arrows Prevents two electrons from having same quantum

numbers

Which hog rule is this?

Hund’s Rule

Every orbital of the same energy is singly occupied before any orbital is doubly occupied

Electrons have the same spin

Second electrons added have opposite spins

Which hog rule is this?

PART 4

Writing Electron Configurations

Electron Configuration Diagonal Rule Starting with the top

arrow, follow the arrows one by one in the direction they point, listing the sublevels as you pass through them.

Stop when you get to the sublevel you need.

Electron Orbital Diagram3d ___ ___ ___ ___ ___4s ___3p ___ ___ ___3s ___2p ___ ___ ___2s ___1s ___

Example: Fill Orbitals w/ 7 electrons3d ___ ___ ___ ___ ___4s ___3p ___ ___ ___3s ___2p ___ ___ ___2s ___1s ___

Review:1. How many electrons fill an s orbital?

2. How many electrons fill a p orbital ?(remember subshells…)

3. How many electrons fill a d orbital?

4. How many electrons fill an f orbital?

Example: Cl3d ___ ___ ___ ___ ___4s ___3p ___ ___ ___3s ___2p ___ ___ ___2s ___1s ___

Give the final E.C:

With a partner:Examples: Give the E.C

H He Li Be B C N F

No more…Make it stop!@!!!! Write the electron configuration for Barium:

Ahhhhhhhhhh!!! Too many electrons!!

But wait…there’s a shortcut…

Noble gas / shorthand configuration: Find the nearest noble gas that came before the

element you are interested in Write the symbol of that noble gas in [brackets] Write the configuration as normal from there…

Examples: Sb

Stop & Practice E.C. Worksheet

All Together Now… Mendeleev didn’t know quantum numbers

BUT…our periodic table is related to HOW electrons fill the levels in the different shells

Blocks s block

Groups 1 & 2 p Block

Groups 3 – 8 d block

Transition Elements f Block

Rare earth metals

It ends w/…

Another Example: Ba (shorthand)

Stop & Practice

Patterns in Electron Configuration Worksheet

ColumnsElements have similar properties

Why?Similar ground state electron configurations

ExamplesNoble gases

Complete sublevel Favorable - do not react

Halogens One electron short of completely filled sublevel

Readily react with elements who have a single electron