Assuming the experimental mass of $^{12}_{6}C$ as $12 \text{ u}$, the mass defect of $^{12}_{6}C$ atom is . . . . . . $\text{u}$. (Mass of proton $= 1.00727 \text{ u}$, mass of neutron $= 1.00866 \text{ u}$).

Binding energy per nucleon of ${ }_1^2 H$ and ${ }_2^4 He$ are $1.1 \ MeV$ and $7.0 \ MeV$ respectively. Energy released in the process ${ }_1^2 H + { }_1^2 H \rightarrow { }_2^4 He$ is: (in $MeV$)

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.

The binding energy per nucleon of a nucleus ${}_Z X^A$ at rest is $6 \ MeV$. It undergoes $\beta^-$ decay as shown below:
${}_Z X^A \to {}_{Z+1} Y^A + {}_{-1}^0 e + \bar{\nu}$
The total kinetic energy $(K.E.)$ of the products is $3 \ MeV$. The binding energy per nucleon of $Y$ (in $MeV$) is:

Draw conclusions from the two main features of the graph of binding energy per nucleon versus the atomic mass number $(A)$.

If $M(A, Z)$,$M_p$,and $M_n$ represent the masses of the nucleus ${}_{Z}^{A}X$,proton,and neutron in $u$ units respectively $(1u = 931.5 \, MeV/c^2)$,and $BE$ represents the binding energy in $MeV$,then which of the following relations is correct?