Orbitals

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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 (n1, 2, 3, )
Shape (s, p, d, f, )
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Allowed Orbitals

• The probability density can only take certain
  shapes at each n energy level, or main shell

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ENERGY
4f ___ ___ ___ ___ ___ ___
___ 4d ___ ___ ___ ___ ___ 4p
___ ___ ___ 4s ___
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• 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

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What type of orbital is this?

1. s
2. pz
3. dxy
4. dxz

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Which type of orbital cant exist?

1. 1px
2. 2px
3. 2s
4. 3dxy

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NODES- Where electrons dont go
Spherical Nodes
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Hydrogen
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You too can play with hydrogen
http//homepages.ius.edu/kforinas/physlets/quantum
/hydrogen.html
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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

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Quantum Numbers and Orbitals
nshell, energy level
lsubshell, shape
mlone for each orbital N, l
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Nodes, Revisited

• of planar nodes l
• of spherical nodes n l 1
• Total nodes n 1
• Example 3d orbital

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What orbital has these quantum numbers?n 3, l
2, ml -1

1. 4p
2. 3d
3. 3p
4. 1d
5. 2f

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What are the quantum numbers for the 5dxy orbital?

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

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Which is not a valid set of quantum numbers?

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

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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
• Hunds Rule
• Electrons only pair after all orbitals at an
  energy level have 1 electron
• Madelungs Rule
• Orbitals fill in the order of the value of n l

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Orbital Filling Order
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ENERGY
4f ___ ___ ___ ___ ___ ___
___ 4d ___ ___ ___ ___ ___ 4p
___ ___ ___ 4s ___
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• 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