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

[SteveDC]

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

 

[DrClaude]

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.

 

[SteveDC]

Great, thanks. And cheers for the tip, the holes method is much quicker!