Radial Function

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Radial Function
1s
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Wave Functions and Orbitals
The lobes of orbitals are sometimes
identified with the numerical sign of the wave
function.
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ungerade
gerade
ungerade
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Electronic ConfigurationTerm Symbols

• Edward A. Mottel
• Department of Chemistry
• Rose-Hulman Institute of Technology

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Four Quantum Numbers

• Each electron in an atom can be described
  uniquely by the four quantum numbers.

• Three rules involving quantum numbers
• Pauli Exclusion Principle
• Aufbau Principle
• Hund's Rule

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Pauli Exclusion Principle

• Only one electron in an atom may have the same
  four quantum numbers.

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Aufbau Principle

• In the ground state, electrons fill in the lowest
  available energy state (orbital) first

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Hund's Rule

• If more than one electron occupies a degenerate
  set of orbitals (orbitals of the same energy),
  then the electrons will fill in such a way as to
  maximize the number of orbitals filled.

• It is more stable for the spin of the electrons
  to be aligned in the same direction.

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Electron Filling Pattern
1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p
5d 5f 5g 6s 6p 6d 6f 6g 6h 7s 7p
1s
2s
2p 3s
3p 4s
3d 4p 5s
4d 5p 6s
4f 5d 6p 7s
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Hund's Rule
Why is it more stable for electrons to have the
same spin than opposite spins?
exchange energy
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Hund's Rule
Why is it less stable for electrons to be in the
same orbital?
electrons occupy the same region of space
Coulombic repulsion energy
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?c
?e
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Exceptions to Electron Filling

• There are two exceptions to the electron filling
  pattern in the first 40 elements.
• Chromium
• Copper

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Chromium
24 electrons
What is the expected (incorrect)
electronic configuration for chromium?
Why might this exception occur?
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Copper
29 electrons
What is the expected (incorrect)
electronic configuration for copper?
Why might this configuration be more stable than
4s2 3d9?
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Exceptions
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Why is the electron filling pattern
different from the electron loss pattern?
V 1s2 2s2 2p6 3s2 3p6 4s2 3d3
V3 1s2 2s2 2p6 3s2 3p6 3d2
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R.L. Rich, Periodic Correlations, 1965 Miessler
Tarr, 3rd Ed, pg 42
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Term Symbols
Spectroscopists use the word term to describe the
energies involved in an electronic transition.
Note this calculation only works for hydrogen
with one electron!
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Term Symbols
Term symbols are an abbreviated description of
the energy, angular momentum and spin of an atom
in a particular state.
d-d electronic transitions are responsible
for the color of metal ions.
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Term SymbolsAngular Momentum and Spin State
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Term SymbolsMultiplicity
MS spin angular momentum 2S 1
net electron spin (S)
net electrons in same direction
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Term Symbols
Obeying the Pauli Exclusion Principle, but
allowing the d-electrons of a vanadium(III)
ion to occupy any other legal patterns, how many
different patterns could exist and what would be
the magnetic properties of each pattern?
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V3 1s2 2s2 2p6 3s2 3p6 3d2
Some examples
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Microstates
How many microstates are possible?
45 microstates
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Ms
3F
triplet F
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Ms
3F
3P
triplet P
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Ms
3F
3P
1G
singlet G
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Ms
3F
3P
1G
1D
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Ms
3F
3P
1G
1D
1S
3F is the ground state (highest MS, ML)
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