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 nucleus
Electrons 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


Electrons can go to a higher or lower energy
level


Aka rungs of a ladder
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 = λν
C = 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 Energy
Lower Freq = Less Energy
E=hxv
E = energy (joules – J)
H = Plank’s constant = 6.626E-34 Js
v = 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
=hxv
 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?
Emission Spectra Lab
Look at the gas tubes and follow directions
provided.
Continuous Spectrum v. Line
Spectrum
 What
Lab?
did you observe in the Emission
Light has Wave-Particle Duality
(& so do electrons)
 Particle

Depends on experiment / what we try to observe
 Throws

& Wave-like Nature
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 Problem
Place 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 2
Quantum 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
 Describes
energy level
values)


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
 Possible

spatial orientation (x, y, z, plane)
Values: - l to + l
Examples: if it is a d orbital
d orbital:
l=
ml =
Example: p-orbital
n=2
l=
ml =
This means, there are _______ p-orbitals and
that they are in three directions (x, y, z
axes):
What orbital corresponds to :
n=2
l=1
ml = 0
Energy level =
Sublevel = _____ - orbital
Orientation:
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)
s
1
p
3
d
5
f
7
How Many Electrons in
Shape
Principle Quantum
Number
(n)
1
2
3
4
5
6
7
Angular
Momentum
Quantum Number
(sublevels)
(l)
Shapes of
Sublevels
# electrons (2n2)
Principle Quantum
Number
(n)
Angular Momentum
Quantum Number
(sublevels)
(l)
Shapes of Sublevels
# electrons (2n2)
1
0
s
2
2
0, 1
sp
8
3
0, 1, 2
spd
18
4
0, 1, 2, 3
spdf
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
STOP
Do 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 Diagram
3d ___ ___ ___ ___ ___
4s ___
3p ___ ___ ___
3s ___
2p ___ ___ ___
2s ___
1s ___
Example: Fill Orbitals w/ 7
electrons
3d ___ ___ ___ ___ ___
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: Cl
3d ___ ___ ___ ___ ___
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!!!
 But
wait…there’s a shortcut…
 Noble



Too many electrons!!
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


p Block


Groups 3 – 8
d block


Groups 1 & 2
Transition Elements
f Block

Rare earth metals
It ends w/…
Another Example: Ba
(shorthand)
Stop & Practice
 Patterns
in Electron Configuration
Worksheet
Columns
 Elements
have similar properties
 Why?
 Similar
ground state electron configurations
 Examples
 Noble
gases
 Complete
sublevel
 Favorable - do not react
 Halogens
 One
electron short of completely filled sublevel
 Readily react with elements who have a single electron