Question

How to use Hund's third rule for excited electronic configurations?

Answer 1

Hund third rule states:

For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number J (for the operator J=L+S) lies lowest in energy. If the outermost shell is more than half-filled, the level with the highest value of Jm is lowest in energy.

I can't understand how to apply this rule to excited electronic configuration (I'm aware that Hund's do not work perfectly with excited electronic configuration but I wonder if this is the case).

In particular I don't understan what is the "half-filled" outermost "shell" when more than one "subshell" is involved (as in excited configuration). For example for the excited Neon triplet state

(1s)2(2s)2(2p)5(3s)1

We have S=1 and L=1. It turns out that the J to chose between 0 and 1 is J=0, but I don't understand why, since here there is the subshell 2pwith one electron missing (and therefore it is "more than half filled"), and the next subshell 3s with one electron only (exactly "half filled"). Also if I consider the two subshells (2p+3s) thogheter they are "more than half filled" (there are 6 electron over the 6+2=8 that can be allocated in total)

Answer 2

According to Hund's rule, all orbitals will be singly occupied before any is doubly occupied. Therefore, two p orbital get one electron and one will have two electrons. Hund's rule also stipulates that all of the unpaired electrons must have the same spin.

Hope its help u