Vanadium $($V$)$ has atomic number Z$=23.$

$($a$)$ Determine the electron configuration of the ground state of vanadium. Assume the

sub$-$shells are filled in the order $1$s$,2$s$,2$p$,3$s$,3$p$,4$s$,3$d etc.

$($b$)$ Determine the quantum numbers S$,$ L and J for the ground state of vanadium and state

the spectroscopic term.