Find the gratest possible values of total angular momenta and the corresponding spectral designation of the term
(a) of a `Na` atom whose valence electron possesses the principle quantum number `n=4`,
(b) of an atom with elctronic configuration of the term.

Explanation

(a) For the `Na` atoms the valence electron has principle quantum number `n=4`, and the possible values of orbital angular momentum are `l=0, 1,2,3 so l_(max)=3`. The state is `.^(2)F`, maximum value of `J` is `(7)/(2)`
Thus the state with maximum angular momentum will be
For this state `M_(max)=ħsqrt((7)/(2).(9)/(2))=(ħsqrt(63))/(2)`
(b) For the atom with electronic configuration `1s^(2) 2p 3d`. There are two inequivalent valence electrons. The total orbital angular moments will be `1,2,3` so we pick `l=3`. The total spin angular momentum will be `s=0,1` so we pick up `s=1`. Finally `J` will be `2,3,4` so we pick up `4`. Thus maximum angular momentum stare is
`.^(3)F_(4)`
For this state `M_(max)= ħsqrt(4xx5)=2 ħsqrt(5)`.