For a nucleus ${ }_Z^A X$ having mass number $A$ and atomic number $Z$:
$A.$ The surface energy per nucleon $(b_s) = a_1 A^{2/3}$
$B.$ The Coulomb contribution to the binding energy $b_c = -a_2 \frac{Z(Z-1)}{A^{4/3}}$
$C.$ The volume energy $b_v = a_3 A$
$D.$ Decrease in the binding energy is proportional to surface area.
$E.$ While estimating the surface energy,it is assumed that each nucleon interacts with $12$ nucleons,($a_1, a_2$ and $a_3$ are constants)
Choose the most appropriate answer from the options given below:

Calculate the energy equivalent of $1\; g$ of substance.

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.

Consider the nuclear reaction $X^{200} \rightarrow A^{110} + B^{90}$. If the binding energy per nucleon for $X$,$A$,and $B$ is $7.4 \, MeV$,$8.2 \, MeV$,and $8.2 \, MeV$ respectively,then the amount of energy released is .......... $MeV$.

Degenerate electron pressure will not be sufficient to prevent the core collapse of a white dwarf if its mass becomes $n$ times the solar mass. The value of $n$ is:

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