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 $\mathrm{E}_{\mathrm{b}}^{\mathrm{p}}$ and the binding energy of a neutron be $\mathrm{E}_{\mathrm{b}}^{\mathrm{n}}$ in the nucleus. Which of the following statement (s) is(are) correct?
Select ALL correct options:
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
$\mathrm{E}_{\mathrm{b}}^{\mathrm{p}}-\mathrm{E}_{\mathrm{b}}^{\mathrm{n}}$ is positive.
D
$\mathrm{E}_{\mathrm{b}}^{\mathrm{p}}$ increases if the nucleus undergoes a beta decay emitting a positron.
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