The document summarizes the quantum mechanical model of the atom. It describes how electrons are located in specific energy levels called orbitals, which are regions where electrons are most likely to be found. The location of electrons is determined by four quantum numbers - principal, azimuthal, magnetic, and spin. Electrons fill these orbitals based on specific rules, such as the Aufbau principle and Hund's rule, resulting in unique electron configurations for each element.

1. Electron Orbitals
Cartoon courtesy of lab-initio.com

2. The Bohr Model of the Atom
I pictured electrons
orbiting the nucleus much
like planets orbiting the
sun.
But I was wrong! They’re
more like bees around a
hive.
Neils Bohr

3. DeBroglie Model
- Since light waves can
have a particle behavior
(as shown by Einstein),
then it follows that
particles could exhibit a
wave behavior.
- Saw the electron as a
wave.

4. Schrodinger and His Cat
•First to propose the idea of electron duality.
•Proposed classic thought experiment involving a
cat in a box.
•The electron is simultaneously a particle and a
wave but cannot be observed in this state.
-When you observe it the electron adopts one
state or the other.

11. Heisenberg Uncertainty Principle
“One cannot simultaneously
determine both the position
and momentum of an electron.”
You can find out where the
electron is, but not where it
is going.
OR…
You can find out where the
Werner electron is going, but not
Heisenberg where it is!

12. Quantum Mechanical
Model of the Atom
Mathematical laws can identify the
regions outside of the nucleus
where electrons are most likely to
be found.
These laws are beyond the scope of
this class…

13. Quantum Mechanical
Model of the Atom

14. Quantum Mechanical
Model of the Atom
•As in the the deBroglie and Bohr Models the
electrons energy is quantized into distinct
levels.
•As the atom is excited electrons move into
higher levels (further from nucleus) and vice
versa.
•The Quantum Mechanical model, however,
makes no attempt to predict the path of the
electron (Heisenburg).
•It does define the electrons most probable
location based on a set of rules.

15. Levels of Organization
•The Quantum Mechanical
model still relies on the idea
of quantized energy levels
HOWEVER each energy level
is further subdivided into
probability zones.
oCalled Orbitals
oThe larger the energy
level the more probability
zones it can contain.
You add a new set of
orbitals with each
successive energy
level.

16. Four Quantum Numbers
• The Quantum Mechanical Model describes the
location of each electron based upon successive
levels of organization called Quantum Numbers.
1. Principal Quantum Number
2. Orbital Quantum Number
3. Magnetic Quantum Number
4. Spin Quantum Number
• Each electron within the atom is assigned a
unique combination of quantum numbers based
upon the location of it’s electrons
– The 4 quantum numbers provide the specific
location of each electron. Similar to an
address.

18. Electron Energy Levels (Shell)
•First level of organization.
•Similar to Bohr Model.
•The shell denotes the probable
distance of the electron from the
nucleus.
•Principle Quantum Number (N):
•Indicates the relative size and
energy of a shell.
•Denoted as “N”
•As N increases the energy
level becomes larger and the
electron spends more time
farther from the nucleus.
•Not evenly spaced.

19. # of Electrons in Energy Levels
The larger the shell the
more electrons it can hold. Maximum # of
electrons per shell
As “N” increases so does the 1st shell: 2
maximum number of electrons
2nd shell: 8
that can be in the shell.
3rd shell: 18
Number of electrons 4th shell: 32
that can fit in a
5th shell: 50
shell:
2n 2

21. Orbital Sub-Levels
PRINCIPAL SUB LEVELS
ENERGY
LEVELS
4 •Each main energy level (shell)
INCREASING ENERGY / DISTANCE FROM NUCLEUS
can be subdivided into sublevels.
•Level 1 was split into 1 sub level
3 •Level 2 was split into 2 sub levels
•Level 3 was split into 3 sub levels
•Level 4 was split into 4 sub levels
2 •These sublevels are known as
orbitals.
1

22. Orbital Quantum Number, ℓ
(Angular Momentum Quantum Number)
Indicates shape of orbital sublevels
ℓ = n-1
ℓ sublevel
0 s
1 p
2 d
3 f
4 g

23. Orbital Shape
Scientists calculate the shape of orbitals
based upon probability.
Orbital Shapes are defined as the surface
that contains 90% of the total electron
probability.

24. ℓ = 0 or S Orbital shape
•Each energy level
contains one
spherical S-Orbital
•Holds 2 Electrons

25. ℓ = 1 or P Orbitals shape
•There are 3 dumbbell-
shaped p orbitals
beginning in n = 2
•Each assigned to its
own axis (x, y and z) in
space.
•Each P orbital contains
two electrons.
2 x 3 = 6 Total

26. ℓ = 2 or D Orbitals shape
Things get a bit more
complicated with the
five d orbitals beginning
in n = 3.
5 x 2 = 10 Electrons Total
To remember the shapes,
think of “double
dumbells”
…and a “dumbell
with a donut”!

27. ℓ = 3 or f Orbitals shape
Beginning in N=4 there are 7 f-orbitals.
7 x 2 = 14 Electrons Total

28. Energy Levels, Orbitals, Electrons
Energy Orbital type Number of Number of Number of
Level in the orbitals Electrons electrons per
(n ) energy level Energy level
(types = n) (2n2)
1 s 1 2 2
2 s 1 2 8
p 3 6
3 s 1 2 18
p 3 6
d 5 10
4 s 1 2 32
p 3 6
d 5 10
f 7 14

31. Magnetic Quantum Number, ml
Indicates the orientation of the
orbital in space.
Values of ml : integers -ℓ to +ℓ
The number of values represents the
number of orbitals.
Example:
for ℓ= 2, ml = -2, -1, 0, +1, +2
Which sublevel does this represent?
Answer: d

33. Electron Spin (ms or s)
Electron spin describes the behavior
(direction of spin: clockwise or
counterclockwise) of an electron
within a magnetic field.
Establishes a limit of 2 electrons per orbital
Possibilities for electron spin:
1 1
OR
2 2

34. Quantum Mechanical Model Summary
Electrons are located in specific
energy levels.
There is no exact path around the
nucleus.
The model estimates the probability
of finding an electron in a certain
position.

35. QUANTUM
NUMBERS
n ---> energy level or shell 1, 2, 3, 4, ...
ℓ ---> subshell or orbitals 0, 1, 2, ... n – 1
ml ---> magnetic orientation -ℓ ... 0 ... +ℓ
ms ---> electron spin +1/2 and -1/2

36. Electron Configurations
__

37. Rules for Filling The Diagram
• Aufbau Principle: Electrons will fill the
lowest energy levels subshell first before
moving to the next higher level.
– The Concert Rule
• Hund's Rule: The most stable arrangement
of electrons is that with the maximum
number of unpaired electrons, all with the
same spin direction. (Electrons won’t double
up if they don’t have to, as long as they
don’t violate the Aufbau Principle)
– The Urinal Etiquette Rule
• Pauli Exclusion Principle: No two electrons
in an atom can have the same set of four
quantum numbers. (Only 2 electrons can be
in an orbital and they must have opposite
spins)
– Two is Company, but Three is a Crowd
Rule

38. Element Configuration Orbital notation Noble gas
notation notation
Lithium 1s22s1 [He]2s1
____ ____ ____ ____ ____
1s 2s 2p
Beryllium 1s22s2 [He]2s2
____ ____ ____ ____ ____
1s 2s 2p
Boron 1s22s22p1 [He]2s2p1
____ ____ ____ ____ ____
1s 2s 2p
Carbon 1s22s22p2 [He]2s2p2
____ ____ ____ ____ ____
1s 2s 2p
Nitrogen 1s22s22p3 [He]2s2p3
____ ____ ____ ____ ____
1s 2s 2p
Oxygen 1s22s22p4 [He]2s2p4
____ ____ ____ ____ ____
1s 2s 2p
Fluorine 1s22s22p5 [He]2s2p5
____ ____ ____ ____ ____
1s 2s 2p
Neon 1s22s22p6 [He]2s2p6
____ ____ ____ ____ ____
1s 2s 2p

39. Orbital filling table

40. Electron configuration of the
elements of the first three series