Question

The only partiallay filled subshell of a certain atom contains three electrons, the basic term of the atom having `L=3`. Using the Hund ruless, 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 of highest orbital angular momentum. This is not possible with `p` elcetrons so we must have `d` electrons for which `L=3` for `3` electrons. For three `f,g` electrons `L gt 3`. Thus we have `3d` electrons. Then as in (6.120) the ground state is
`.^(4)F_(3/2)`