1. Unit 6
Quantum Mechanics

2. + Evolution of Atomic Theory Thomson (plum pudding) Rutherford +
electron
nucleus +
Schrödinger
(Quantum Mechanical Model)
Bohr
(planetary)

3. Bohr Model a.k.a. planetary model Energy levels A specific area
around the
nucleus where
an e- is likely
to be – all e- in
the same energy
level have the
same energy N
Valence shell

4. Bohr Model Pros: Electrons do move around nucleus
Electrons exist in energy levels
Cons:
Electrons do not remain in “orbits”

5. Electron Configuration
Breaking down the electron cloud.
Electron hierarchy
Energy levels (shells)
Subshells (sublevels-s,p,d,f)
Orbitals (clouds)
Each atom has a certain number of energy levels (same as
period number) (Principle Quantum # n)
These energy levels contain a certain number of sublevels.
(Angular Momentum Quantum # l - shape of the orbital)
Each sublevel contains a certain number of orbitals. (n2)

6. Sublevels The number of sublevels an energy level contains is equal to
the energy level number. (Principle Quantum # n)
Example: Potassium is in period 4, which means it has 4 energy
levels and 4 sublevels: (Principle Quantum # 4)
Its 1st energy level has 1 sublevel(s)
Its 2nd energy level has 2 sublevels (s,p)
Its 3rd energy level has 3 sublevels (s,p,d)
Its 4th energy level has 4 sublevels (s,p,d,f)
So, potassium has a total of 10 sublevels.
By analogy, if an atom is a building, each energy level would be
a story. Each sublevel is like a room on that floor.

7. n = # of sublevels per level n2 = # of orbitals per level
Quantum Numbers
Principal
level
n = 1
n = 2
n = 3
Sublevel s s p s p d
Orbital px py pz px py pz
dxy
dxz
dyz
dz2
dx2- y2
n = # of sublevels per level
n2 = # of orbitals per level
Sublevel sets: s-1, p-3, d-5, f-7 7

8. Sublevels Each sublevel has its own shape. (Quantum # l)
The shape is based on calculated probability.
The first sublevel (s - sharp) is sphere shaped.
The second sublevel (p - principal) contains 3 orbitals which are
each dumbbell shaped and follow the X, Y or Z axis.

9. Sublevels
The third sublevel (d - diffuse) contains 5 orbitals which are each
cloverleaf shaped except the last one which is like a dumbbell
with a ring.
Magnetic Quantum Number ( ml )
Orientation of orbital
Specifies the exact orbital within each sublevel
Courtesy Christy Johannesson 9

10. Sublevels
The fourth sublevel (f - fundamental) is too complex to draw in 2D.
Atomic orbital – the shape of space in which an e- of a given
energy level is likely to be.

11. P S D F Sublevels The Periodic Table breaks down into 4 blocks.
Each block represents one of the shapes or sublevels.
That is the shape of the outer sublevel of the valence shell. P S D F

12. P S D F Sublevels Each sublevel has a number!
Numbering sublevels : s & p # = Period #
d # = Period # – 1
f # = Period #- 2 P S D F

13. Sublevels - Practice
What is the name of the sublevel containing the outermost
electron in the following elements?
Lithium 2s
Sulfur 3p
Iron 4s 6s
Erbium

14. Electron Filling 1.Aufbau Principle
Electrons are assigned to energy levels, sublevels and
orbitals based on three principles or rules.
1.Aufbau Principle
Electrons enter the lowest energy level available.
Not necessarily in numerical order.
Example: 3s  3p  4s  3d
Within an energy level, the s sublevel
has the least energy, then p, then d,
then f.

15. Aufbau
The Aufbau diagram follows the Periodic Table read left to right,
top to bottom. Lower energy fills up first.
Note: the valence electrons are in the energy level with the
highest number. Therefore Zirconium’s valence are in 5s, not 4d. P S D F

16. 2. Pauli Exclusion Principle
Each orbital can contain only 2 electrons.
Therefore,
sublevel # of orbitals total electrons held
s e-
p e-
d e-
f e-
Total e- is also equal to the number of elements in one row of
that block. (Formula 2n2 will tell the # of electrons for that energy level)
Example:
1s contains two elements: H & He
2p contains six elements: B, C, N, O, F & Ne
etc.

17. Electron spin
Each e- revolves around the nucleus and rotates on its axis.
They can rotate clockwise or counterclockwise.
The spins are represented by arrows:
Opposite spins will attract, like spins will repel.
This is why a orbital cannot contain more than 2 e-.

18. Quantum Numbers Spin Quantum Number ( ms ) Electron spin  +½ or -½
An orbital can hold 2 electrons that spin in opposite directions. 18

19. 3. Hund’s Rule
When filling a sublevel that has multiple orbitals (p, d, f), put
one e-, having the same spin, in each orbital until each has
one, then start doubling up.

20. Electron Filling
You must draw all the orbitals for a sublevel, even if they
aren’t occupied.
The reason is because the sublevels and orbitals represent
probability. The orbitals show where the e- is likely to be,
not necessarily where it is.

21. Summary!

22. Writing electron configurations:
1) Each electron that is added to an atom is placed in the lowest‐energy
orbital that is available. (Aufbau) The orbitals are filled in the order
which is read off the periodic table when reading in order of atomic
number: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f
2)Each orbital can hold no more than two electrons. Two electrons in the same orbital must have opposite spins
(the Pauli exclusion principle).
3)If two or more orbitals are available at the same energy level and
same sublevel (degenerate orbitals), one electron is placed in each
orbital until the available orbitals are occupied by one electron.
Remember one electron in each orbital before you double up.
(Hund’s Rule)

23. Writing Shorthand
Method of writing e- configuration by skipping the boxes and
arrows and just using numbers and letters.
Example: Carbon 1s22s22p2
# e- in orbital
E level
1s2
Orbital shape

24. Writing Shorthand - Practice
For each element, write its e- configuration in shorthand.
Lithium
1s22s1
Sulfur
1s22s22p63s23p4
Iron
1s22s22p63s23p64s23d6
Erbium
1s22s22p63s23p64s23d104p65s24d105p66s24f12

25. Identify that element 1s22s22p63s23p64s23d9 Copper
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p6
Radon
Magnesium
1s22s22p63s2

26. Noble Gas Shorthand
Electron configurations can get lengthy. We can shorten using
noble gas.
Sulfur
1s22s22p63s23p4
Neon
1s22s22p6
Sulfur
[Ne] 3s23p4

27. Writing Noble Gas Shorthand - Practice
For each element, write its e- configuration in noble gas shorthand.
Beryllium
[He]2s2
Arsenic
[Ar]4s23d104p3
Silver
[Kr]5s24d9
Lead
[Xe]6s24f145d106p2

28. Drawing orbital diagram
Though you have to be able to draw the s, p, d, & f shapes on
the test, there’s a faster way to draw the e- configuration.
Steps for drawing orbital diagram:
1. Using Aufbau, draw a set of boxes to
represent the sublevel (s = 1, p = 3, d = 5, f = 7)
2. Using Pauli and Hund, fill the boxes with arrows to
represent the electrons.
3. Keep going until all e- used up.
Example: Carbon 1s 2s 2p

29. Drawing orbital diagrams - practice
For each element, draw the boxes and arrows.
Make sure to draw all the boxes for a sublevel (even if they’re not used) and
write the name of the sublevel above or below each set of boxes. 1s 2s
Lithium 1s 2s 2p 3s 3p
Sulfur 1s 2s 2p 3s 3p 4s 3d
Iron

30. Identify that element 1s 2s 2p 3s 3p 4s Calcium 1s 2s 2p 3s 3p 4s 3d
Bromine

31. Noble Gas Notation
Electron configurations can get lengthy. We can shorten using
noble gas. 1s 2s 2p 3s 3p
Sulfur 1s 2s 2p
Steps for noble gas
Find previous noble gas
Put noble gas in brackets
Write e- config. for the rest
Neon 3s 3p
Sulfur
[Ne]

32. Noble e- configurations - practice
For each element, draw the boxes and arrows.
Make sure to draw all the boxes for a sublevel (even if they’re not used) and
write the name of the sublevel above or below each set of boxes. 4s 3d
Titanium
[Ar] 5s 4d 5p
Iodine
[Kr] 7s 5f
Uranium
[Rn]

33. Ions Can draw e- configurations (boxes and arrows) and write shorthand
and quantum numbers for ions just like for neutral (ground state)
atoms.
Only difference is ions have gained or lost e- 3s 3p S
[Ne]
[Ne] 3s23p4 3s 3p
S2-
[Ne]
[Ne] 3s23p6 gained 2e-

34. Ions - Practice
Draw e- configurations (boxes and arrows) and write shorthand
and quantum numbers (outermost subshell only)
Ga3+ from Ga 4s 3d 4p Ga
[Ar]
Ga:
[Ar] 4s23d104p1
Ga3+ : [Ar] 3d10 lost 3e- from highest numbered energy level
The highest numbered energy level contains the bonding
electrons or valence electrons.

35. A Lewis symbol (Lewis dot diagram) is a symbol in which the electrons
in the valence shell (outer energy level) of an atom or simple ion are
represented by dots placed around the letter symbol of the element.
Each dot represents one electron. Negative ions gain electrons and
positive ions lose electron.

36. Lewis Dot Diagrams: Number of valence electrons is equal to group #. I II
III IV V VI
VII
VIII
Hydrogen
Oxygen
Chlorine
Chloride ion Cl‐1