Nuclear Forces and Models Questions and Answers

Answer: C

The first four magic numbers are 2, 8, 14, 20.

In a cubical box the levels are \(E \propto n_{x}^{2} + n_{y}^{2} + n_{z}^{2}\) with each \(n \ge 1\). Count the distinct arrangements (degeneracy), and double for the two spin states:

• (1,1,1), sum 3: 1 state, 2 nucleons, total 2.
• (2,1,1) and permutations, sum 6: 3 states, 6 nucleons, total 8.
• (2,2,1), sum 9: 3 states, 6 nucleons, total 14.
• (3,1,1), sum 11: 3 states, 6 nucleons, total 20.

Shell closures, the magic numbers in this model, are therefore 2, 8, 14, 20. The sequence 2, 8, 20, 28 is the observed set from the real nuclear shell model with spin-orbit coupling, which a simple box does not reproduce.

Answer: C

The nuclear force is independent of the nucleons' charge.

Mirror nuclei, such as \(^{3}\)H and \(^{3}\)He or \(^{13}\)C and \(^{13}\)N, have their proton and neutron numbers interchanged. Once the Coulomb energy is allowed for, their energy levels are nearly identical, which shows that the nn and pp interactions are the same: the strong force does not distinguish a proton from a neutron. This is charge symmetry, part of the wider idea of charge independence.

Swapping protons and neutrons leaves spins and parities of the nucleons unchanged, so mirror nuclei say nothing about dependence on spin or parity; and the tiny proton-neutron mass difference is not what the comparison tests.