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 .......... $MeV$.

Answer the following questions:
$(a)$ Are the equations of nuclear reactions 'balanced' in the sense a chemical equation (e.g.,$2H_2 + O_2 \rightarrow 2H_2O$) is? If not,in what sense are they balanced on both sides?
$(b)$ If both the number of protons and the number of neutrons are conserved in each nuclear reaction,in what way is mass converted into energy (or vice-versa) in a nuclear reaction?
$(c)$ $A$ general impression exists that mass-energy interconversion takes place only in nuclear reactions and never in chemical reactions. This is strictly speaking,incorrect. Explain.

If the total binding energies of ${ }_1^2 H ,{ }_2^4 He ,{ }_{26}^{56} Fe$ and ${ }_{92}^{235} U$ nuclei are $2.22, 28.3, 492$ and $1786 \text{ MeV}$ respectively,identify the most stable nucleus of the following.

According to the mass-energy equivalence relation,$9 \times 10^{13} \text{ J}$ of energy can be converted into $\qquad$ maximum mass. [Speed of light $c = 3 \times 10^{8} \text{ m/s}$] (in $\text{ g}$)

The deuteron is bound by nuclear forces just as the $H$-atom is made up of a proton and an electron bound by electrostatic forces. If we consider the force between the neutron and proton in a deuteron as given in the form of a Coulomb potential but with an effective charge $e'$: $F = \frac{1}{4\pi \epsilon_0} \frac{e'^2}{r^2}$,estimate the value of $(e'/e)$ given that the binding energy of a deuteron is $2.2 \text{ MeV}$.

$_{2}He^{3}$ and $_{1}H^{3}$ nuclei have the same mass number. Do they have the same binding energy?