Nucleus $A$ having $Z=17$ and an equal number of protons and neutrons has $1.2 \, MeV$ binding energy per nucleon. Another nucleus $B$ of $Z=12$ has a total of $26$ nucleons and $1.8 \, MeV$ binding energy per nucleon. The difference in binding energy of $B$ and $A$ will be $........... \, MeV$.

If $M(A, Z)$,$M_p$,and $M_n$ denote the masses of the nucleus ${}_Z^AX$,proton,and neutron respectively in units of $u$ $(1u = 931.5 \text{ MeV}/c^2)$,and $BE$ represents its binding energy in $\text{MeV}$,then:

$\gamma$-rays radiation can be used to create an electron-positron pair. In this process of pair production,$\gamma$-rays energy cannot be less than ....... $MeV$.

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.

The masses of a proton, neutron, and helium nucleus are $1.0073\,u$, $1.0087\,u$, and $4.0015\,u$ respectively. The binding energy of the helium nucleus is $.........\,MeV$.

$A$ nucleus of mass $M$ emits a $\gamma$-ray photon of frequency $\nu$. The loss of internal energy by the nucleus is: