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 ___

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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 ___

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What type of orbital is this?

1 2 3 4

5%

56%

36%

3%

1. s2. pz

3. dxy

4. dxz

Which type of orbital can’t exist?

1 2 3 4

25% 25%25%25%1. 1px

2. 2px

3. 2s4. 3dxy

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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 – 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

Orbital Filling Order

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 ___

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