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A level of an atomic term with specified total angular momentum $J$. Without an external field, its $2J+1$ magnetic states remain degenerate in a rotationally invariant Hamiltonian.

Closed subshells have $L=S=0$, so only the open $p$ or $d$ subshell determines each atomic term. Apply Hund's rules in order: maximize $S$, maximize $L$ at that $S$, then choose the lowest $J$ below half filling or the highest $J$ above half filling.

For carbon, the two $2p$ electrons occupy different magnetic atomic orbitals with parallel spins, giving $S=1$. Their largest allowed $M_L$ at that spin is $1+0=1$, so $L=1$, a $P$ term. The $p^2$ subshell is less than half full, giving $J=|1-1|=0$. The ground level is ${}^3{P}_0$.

For vanadium, three parallel-spin $3d$ electrons give $S=3/2$. The largest $M_L$ compatible with the Pauli exclusion principle is $2+1+0=3$, hence $L=3$, an $F$ term. The $d^3$ subshell is less than half full, so $J=3-3/2=3/2$. The ground level is ${}^4{F}_{3/2}$.

For cobalt, the $d^7$ subshell is equivalent to three $d$ holes for the allowed $L,S$ terms, so its maximum-spin, maximum-$L$ term is again ${}^{4}F$. Explicitly, five spin-up electrons fill all $m_l$ values and two spin-down electrons can occupy $m_l=2,1$, giving $M_S=3/2$ and $M_L=3$. Since $d^7$ is more than half full, $J=3+3/2=9/2$. The ground level is ${}^4{F}_{9/2}$.

An electron configuration specifies the occupied one-electron subshells and their populations, such as $1s^{2}2s^{2}2p^2$, without fixing how all orbital and spin angular momenta are coupled.

An atomic term groups states of a configuration with the same $L$ and $S$. An atomic fine-structure level additionally specifies $J$; spin-orbit coupling can split one term into several such levels. In zero external field, a level retains $2J+1$ magnetic substates.

The term symbol iswith letters $S,P,D,F,G,\dots$ denoting $L=0,1,2,3,4,\dots$. The superscript is the spin multiplicity. Without the $J$ subscript, ${}^{2S+1}L$ identifies an atomic term, rather than an individual fine-structure level.

Within a specified electron configuration in the LS coupling regime, Hund's rules select the lowest atomic term as follows. First maximize the total electron spin $S$ subject to the Pauli exclusion principle. Among the terms having that $S$, choose the largest total orbital angular momentum $L$. Finally, spin-orbit coupling places the smallest allowed $J=|L-S|$ lowest for a subshell less than half full, and the largest $J=L+S$ lowest for a subshell more than half full. At half filling the maximum-spin term has $L=0$, hence $J=S$. These rules rank terms within configurations; the exceptional neutral-atom configurations of chromium and copper must also be used.