0. Orbitals Each wave function describes a shape = Orbital
Where an electron can be found/exist
Organized into main shells and subshells
Number of orbitals is different for each subshell type:
s = 1 orbital
p = 3 orbitals
d = 5 orbitals
f = 7 orbitals
Size and Energy
(n=1, 2, 3, … )
Shape
(s, p, d, f, … )

1. “Allowed” Orbitals
The probability density can only take certain shapes at each n energy level, or main shell

3. ENERGY
4f ___ ___ ___ ___ ___ ___ ___
4d ___ ___ ___ ___ ___
4p ___ ___ ___
4s ___ 4
3d ___ ___ ___ ___ ___
3p ___ ___ ___
3s ___ 3
2p ___ ___ ___
2s ___ 2
1, 2, and 3 correspond to the major energy levels (main shells)
At the same main shell level, a p orbital will be at a higher energy than an s orbital
1s ___ 1

4. What type of orbital is this?pz
dxy
dxz 10

5. Which type of orbital can’t exist?
1px
2px 2s
3dxy 10

6. NODES- Where electrons don’t go
Spherical Nodes

7. Hydrogen

8. You too can play with hydrogen…

9. Quantum # Rules
There are four different quantum numbers: n, l, ml, and ms
n, l, and ml are integers
n cannot be zero
l can be 0 to n-1
ml can be anything from –l to l
ms can be +½ or -½

10. Quantum Numbers and Orbitals
n=shell, energy level
l=subshell, shape
ml=one for each orbital
N, l

11. Nodes, Revisited # of planar nodes = l
# of spherical nodes = n – l – 1
Total # nodes = n – 1
Example: 3d orbital

12. What orbital has these quantum numbers? n = 3, l = 2, ml = -14p 3d 3p 1d 2f 10

13. What are the quantum numbers for the 5dxy orbital?
n = 5, l = 2, ml = 0
n = 5, l = -2, ml = 3
n = 4, l = 2, ml = 2
n = 5, l = 3, ml = 0
n = 5, l = 2, ml = -5 10

14. Which is not a valid set of quantum numbers?
n = 4, l = 1, ml = -1
n = 1, l = 0, ml = 0
n = 6, l = 5, ml = -5
n = 2, l = 2, ml = 1
n = 3, l = 2, ml = 2 10

16. Rules for filling orbitals
Pauli Exclusion Principle
No two electrons can have the same 4 quantum numbers
An orbital has a maximum of 2 electrons of opposite spin
Aufbau/Build-up Principle
Lower energy levels fill before higher energy levels
Hund’s Rule
Electrons only pair after all orbitals at an energy level have 1 electron
Madelung’s Rule
Orbitals fill in the order of the value of n + l

17. Orbital Filling Order

18. ENERGY
4f ___ ___ ___ ___ ___ ___ ___
4d ___ ___ ___ ___ ___
4p ___ ___ ___
4s ___ 4
3d ___ ___ ___ ___ ___
3p ___ ___ ___
3s ___ 3
2p ___ ___ ___
2s ___ 2
1, 2, and 3 correspond to the major energy levels (main shells)
At the same main shell level, a p orbital will be at a higher energy than an s orbital
1s ___ 1