The binding energy per nucleon versus mass number curve for nuclei is shown in the figure. $W, X, Y$ and $Z$ are four nuclei indicated on the curve. The process that would release energy is

Two nuclei of mass number $3$ combine with another nucleus of mass number $4$ to yield a nucleus of mass number $10$. If the binding energy per nucleon for the mass numbers $3$, $4$, and $10$ are $5.6 \text{ MeV}$, $7.4 \text{ MeV}$, and $6.1 \text{ MeV}$, respectively, then in the process, $\Delta Mc^2 = . . . . . . \text{ MeV}$.

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 $A^{-1/3}$ 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.

Given the masses of various atomic particles $m_{p} = 1.0072 \ u$,$m_{n} = 1.0087 \ u$,$m_{e} = 0.000548 \ u$,$m_{\bar{v}} = 0$,and $m_{d} = 2.0141 \ u$,where $p \equiv$ proton,$n \equiv$ neutron,$e \equiv$ electron,$\bar{v} \equiv$ antineutrino,and $d \equiv$ deuteron. Which of the following processes is allowed by momentum and energy conservation?

One million electron volt $(1\,MeV)$ is equal to

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