$A$ nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass. If $C$ is the speed of light,and $E_1$ is the binding energy per nucleon for the parent nucleus and $E_2$ is that for the daughter nuclei,then:

The binding energy per nucleon for $C^{12}$ is $7.68 \text{ MeV}$ and that for $C^{13}$ is $7.5 \text{ MeV}$. The energy required to remove a neutron from $C^{13}$ is ......... $\text{MeV}$.

The mass of a nucleus,a neutron,and a proton are $M$,$M_n$,and $M_p$ respectively. Then which of the following is true?

Assume that the nuclear binding energy per nucleon $(B/A)$ versus mass number $(A)$ is as shown in the figure. Use this plot to choose the correct choice$(s)$ given below.
Figure: $222706-q$
$(A)$ Fusion of two nuclei with mass numbers lying in the range of $1 < A < 50$ will release energy.
$(B)$ Fusion of two nuclei with mass numbers lying in the range of $51 < A < 100$ will release energy.
$(C)$ Fission of a nucleus lying in the mass range of $100 < A < 200$ will release energy when broken into two equal fragments.
$(D)$ Fission of a nucleus lying in the mass range of $200 < A < 260$ will release energy when broken into two equal fragments.

Derive the formula for the binding energy of a nucleus by explaining the mass defect of the nucleus and write the formula for the binding energy per nucleon.

If the binding energy per nucleon for $\,_3^7\,Li\,\,$ and $\,_2^4\,\,He$ are $5.60 \,MeV$ and $7.06 \,MeV$ respectively, then the energy of the proton in the reaction $p\,\, + \,\,_3^7\,\,Li\,\, \to \,\,2\,_2^4\,\,He$ must be .......... $MeV$.