Question

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.

Answer 1

The Correct Option is A, B, D

$E_b^p-E_b^n$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus,
$E_b^p-E_b^n$ is proportional to $A^{-\frac{1}{3}}$ where $A$ is the mass number of the nucleus and 
$E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.