Answer
(a) An impossible nucleus
(b) A nuclear ground state
(c) An excited nuclear state
Work Step by Step
1. Each of the cases deals with the first three allowed energy levels in the nuclear shell model , n=1, n=2 and n=3.
2. According to Pauli exclusion principle, n=1 level can accommodate maximum 2 nucleons(one with up spin and one with down spin), n = 2 level can accommodate maximum 4 nucleons (two with up spins and two with down spins), and n = 3 level can accommodate maximum 2 nucleons (one with up spin and one with down spin).
3. In figure (a), there are 3 neutrons in n = 1 level which is not allowed making it impossible.
4. In figure (b), the levels are filled according to Pauli principle and no lower energy level is kept empty while filling higher energy shell. So, it is a ground state.
5. In figure (c), Pauli principle is followed but one neutron is put at n=3 level when n = 2 level could still accommodate one neutron. So, it is an excited state
