Solving Erbium's Ground State w/ Hund's Rules

  • #1
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I have the solution for this problem but don't understand it.

1. Homework Statement

Use Hund's rules to calculate the ground state of erbium with electron configuration [Xe]4f126s2

Homework Equations


Hunds Rules:
1. Maximise S (within Pauli)

2. Maximise L (within Pauli)

3. Min J (for less than half-filled orbitals) or Max J (for more than half-filled orbitals)

The Attempt at a Solution


So I used these rules on the 12 electrons in unfilled f orbital and I arrived at S=1, L=5, and therefore J=S+L=6 but the solution which I have been given is: S=3, L=9, J=12

Can anyone confirm if the solution is correct and where I am going wrong?

Thanks
 
  • #2
So I used these rules on the 12 electrons in unfilled f orbital and I arrived at S=1, L=5, and therefore J=S+L=6 but the solution which I have been given is: S=3, L=9, J=12
Your solution is correct.

For more than half-filled shells, it is easier to work with holes than with electrons: f12 and f2 generate the same terms. That will tell you quickly what the solution is.
 
  • #3
Great, thanks. And cheers for the tip, the holes method is much quicker!
 

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