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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, … )
“Allowed” Orbitals
The probability density can only take certain shapes at each n energy level, or main shell
1s ___11
2p ___ ___ ___2s ___22
3d ___ ___ ___ ___ ___
3p ___ ___ ___3s ___
33
ENERGY
•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
4f ___ ___ ___ ___ ___ ___ ___ 4d ___ ___ ___ ___ ___ 4p ___ ___ ___
4s ___
44
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
Nodes, Revisited
# of planar nodes = l# of spherical nodes = n – l – 1Total # nodes = n – 1
Example: 3d orbital
What orbital has these quantum numbers?n = 3, l = 2, ml = -1
1 2 3 4 5
20% 20% 20%20%20%1. 4p2. 3d3. 3p4. 1d5. 2f
10
What are the quantum numbers for the 5dxy orbital?
1 2 3 4 5
20% 20% 20%20%20%
10
1. n = 5, l = 2, ml = 0
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
Which is not a valid set of quantum numbers?
1 2 3 4 5
20% 20% 20%20%20%
10
1. n = 4, l = 1, ml = -1
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
Rules for filling orbitals
1. Pauli Exclusion PrincipleNo two electrons can have the same 4 quantum numbersAn orbital has a maximum of 2 electrons of opposite spin
2. Aufbau/Build-up PrincipleLower energy levels fill before higher energy levels
3. Hund’s RuleElectrons only pair after all orbitals at an energy level have
1 electron
4. Madelung’s RuleOrbitals fill in the order of the value of n + l
1s ___11
2p ___ ___ ___2s ___22
3d ___ ___ ___ ___ ___
3p ___ ___ ___3s ___
33
ENERGY
•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
4f ___ ___ ___ ___ ___ ___ ___ 4d ___ ___ ___ ___ ___ 4p ___ ___ ___
4s ___
44