Orbitals
 Each wave function describes a shape = Orbital
 Where an electron can be found/exist
 Organized into main shells and subshells
Size and Energy
(n=1, 2, 3, … )

Shape
(s, p, d, f, … )
Number of orbitals is different for each subshell type:
s = 1 orbital
 p = 3 orbitals
 d = 5 orbitals
 f = 7 orbitals

“Allowed” Orbitals
 The probability density can only take certain shapes
at each n energy level, or main shell
4
3
ENERGY
2
1
4f ___ ___ ___ ___ ___ ___ ___
4d ___ ___ ___ ___ ___
4p ___ ___ ___
3d ___ ___ ___ ___ ___
4s ___
3p ___ ___ ___
3s ___
2p ___ ___ ___
2s ___
•1, 2, and 3 correspond to the
major energy levels (main shells)
1s ___
•At the same main shell level, a p
orbital will be at a higher energy
than an s orbital
What type of orbital is this?
1. s
56%
2. pz
36%
3. dxy
4. dxz
5%
1
3%
2
3
4
Which type of orbital can’t exist?
1. 1px
25%
25%
25%
2
3
25%
2. 2px
3. 2s
4. 3dxy
1
4
10
NODES- Where electrons don’t go
Spherical Nodes
Hydrogen
You too can play with hydrogen…
http://homepages.ius.edu/kforinas/physlets/quantum/hydrogen.html
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
Quantum Numbers and Orbitals
Nodes, Revisited
 # of planar nodes =
l
 # of spherical nodes = n – l – 1
 Total # nodes = n – 1
 Example: 3d orbital
What orbital has these quantum numbers?
n = 3, l = 2, ml = -1
1. 4p
20%
20%
20%
2
3
20%
20%
2. 3d
3. 3p
4. 1d
5. 2f
1
4
5
10
What are the quantum numbers for the 5dxy orbital?
1. n = 5, l = 2, ml = 0
20%
20%
20%
2
3
20%
20%
2. n = 5, l = -2, ml = 3
3. n = 4, l = 2, ml = 2
4. n = 5, l = 3, ml = 0
5. n = 5, l = 2, ml = -5
1
4
5
10
Which is not a valid set of quantum numbers?
1. n = 4, l = 1, ml = -1
20%
20%
20%
2
3
20%
20%
2. n = 1, l = 0, ml = 0
3. n = 6, l = 5, ml = -5
4. n = 2, l = 2, ml = 1
5. n = 3, l = 2, ml = 2
1
4
5
10
Rules for filling orbitals
1.
Pauli Exclusion Principle
No two electrons can have the same 4 quantum numbers
An orbital has a maximum of 2 electrons of opposite spin
2. Aufbau/Build-up Principle
Lower energy levels fill before higher energy levels
3. Hund’s Rule
Electrons only pair after all orbitals at an energy level have 1 electron
4. Madelung’s Rule
Orbitals fill in the order of the value of n + l
Orbital Filling Order
4
3
ENERGY
2
1
4f ___ ___ ___ ___ ___ ___ ___
4d ___ ___ ___ ___ ___
4p ___ ___ ___
3d ___ ___ ___ ___ ___
4s ___
3p ___ ___ ___
3s ___
2p ___ ___ ___
2s ___
•1, 2, and 3 correspond to the
major energy levels (main shells)
1s ___
•At the same main shell level, a p
orbital will be at a higher energy
than an s orbital