Hund's Rule for Determining Term Symbol Energy Order

[Mr_Allod]

Homework Statement:

Use Hund's rules to determine the energy order of the term symbols of a $d^9f^1$ electron configuration.

Relevant Equations:

None

Hello there, for the above question I have no issue finding the term symbols but I am a little unsure about employing Hund's rules to the electron configuration, particularly those referring to the energies based on the total angular momentum J. These state:

- In a less than $\frac12$-filled subshell Lowest J-value is Lowest energy
- In a more than $\frac12$-filled subshell Highest J-value is Lowest energy

For configurations where only one orbital is involved such as $p^5,d^3$ etc. this is easy to apply. But what about configurations where two orbitals are involved such as $p^5d^1$ or $d^9f^1$? In these cases to which orbital do we apply the less/more than $\frac 12$-filled condition?

 

[DrClaude]

Hund's rules apply only to equivalent electrons. It would work for d⁹, but applying it to d⁹f¹ is iffy.

In any case, considering that this is the problem you were given, the equivalent electrons being the d⁹, I would consider the subshell as more than half-filled.

 

[Mr_Allod]

Hund's rules apply only to equivalent electrons. It would work for d⁹, but applying it to d⁹f¹ is iffy.

In any case, considering that this is the problem you were given, the equivalent electrons being the d⁹, I would consider the subshell as more than half-filled.

Thank you for the answer, I've had a very hard time finding a straight answer to this question anywhere so it's nice to have something to go on.