Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / A7

For nonequivalent p-s and p-p term counting, the closed $3s^2$ shell has $L=S=0$. For $3p4s$, the open orbitals give $L=1$ and $S=0,1$, henceHund's rules predict the order ${}^3{P}_0<{}^3{P}_1<{}^3{P}_2<{}^1{P}_1$.

For $3p4p$, the electrons are in nonequivalent orbitals. All $L=0,1,2$ and $S=0,1$ combinations are allowed:Applying maximum spin first, maximum orbital angular momentum next, and smallest $J$ first for these less-than-half-filled open subshells gives the qualitative orderingThe state counts are $12$ for $3p4s$ and $36$ for $3p4p$. Imposing the equivalent-$p^2$ restrictions would incorrectly discard allowed terms. These are Hund-rule predictions; exact interleavings in a real excited configuration require the actual Coulomb and spin-orbit matrix elements.