$m_{p}$ and $m_{n}$ are the masses of a proton and a neutron, respectively. For an element of mass $M$ having $Z$ protons and $N$ neutrons, which of the following is true?

Deuteron is a bound state of a neutron and a proton with a binding energy $B = 2.2 \, MeV$. $A$ $\gamma$-ray of energy $E$ is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the $n$ and $p$ move in the direction of the incident $\gamma$-ray. If $E = B$,show that this cannot happen. Hence,calculate how much bigger than $B$ must $E$ be for such a process to happen.

Write and explain Einstein's theory of special relativity in the context of mass-energy equivalence.

How much energy is released when $1 \,g$ of hydrogen is converted into $0.993 \,g$ of helium?

The binding energy $(BE)$ per nucleon for an element is $7.14 \text{ MeV}$. If the total $BE$ of the element is $28.6 \text{ MeV}$,then the number of nucleons in the element is:

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei $_{20}^{41} Ca$ and $_{13}^{27} Al$ from the following data:
$m(_{20}^{40} Ca) = 39.962591 \; u$
$m(_{20}^{41} Ca) = 40.962278 \; u$
$m(_{13}^{26} Al) = 25.986895 \; u$
$m(_{13}^{27} Al) = 26.981541 \; u$
(Given mass of neutron $m_n = 1.008665 \; u$)