Question

The only partially filled subshell of a certain atom contains three electrons, the basic term of the atom having L = 3. Using the Hund rules, write the spectral symbol of the ground state of the given atom.

Answer 1

With three electrons S=3/2 and the spin part is totally symmetric. It is given that the basic term has L = 3 so L = 3 is the state o f highest orbital angular momentum. This is not possible with p electron so we must have d electrons for which L = 3 for 3 electrons. For three f, g electrons L > 3. Thus we have 3 d electrons. Then as in (6.120) the ground state is

⁴F_3/2