The binding energy per nucleon of ${ }_5 B ^{10}$ is $8.0 \,MeV$ and that of ${ }_5 B ^{11}$ is $7.5 \,MeV$. The energy required to remove a neutron from ${ }_5 B ^{11}$ is .......... $MeV$.

Given below are two statements:
Statement $I$: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement $II$: For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below:

The mass of an $\alpha$-particle is

$A$ free nucleus of mass $24 \, amu$ emits a gamma photon (when initially at rest). The energy of the photon is $7 \, MeV$. The recoil energy of the nucleus in $keV$ is:

The mass of a $_3^7Li$ nucleus is $0.042 \, u$ less than the sum of the masses of its constituent nucleons. The binding energy per nucleon of the $_3^7Li$ nucleus is approximately ......... $MeV$.

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.