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The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be \( E_{b}^{p} \) and the binding energy of a neutron be \( E_{b}^{n} \) in the nucleus.
Which of the following statement(s) is(are) correct?
(a) \( E_{b}^{p}-E_{b}^{n} \) is proportional to \( Z(Z-1) \) where \( Z \) is the atomic number of the nucleus.
(b) \( E_{b}^{p}-E_{b}^{n} \) is proportional to \( A^{-\frac{1}{3}} \) where \( A \) is the mass number of the nucleus.
(c) \( E_{b}^{p}-E_{b}^{n} \) is positive.
(d) \( E_{b}^{p} \) increases if the nucleus undergoes a beta decay emitting a positron.
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