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?

$A$ plot of the number of neutrons $(N)$ against the number of protons $(Z)$ for stable nuclei exhibits upward deviation from linearity for atomic number $Z > 20$. For an unstable nucleus having an $N/Z$ ratio less than $1$,the possible mode$(s)$ of decay is(are):
$(A)$ $\beta^{-}$-decay ($\beta$ emission)
$(B)$ Orbital or $K$-electron capture
$(C)$ Neutron emission
$(D)$ $\beta^{+}$-decay (positron emission)

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.

$A$ nuclide $1$ is said to be the mirror isobar of nuclide $2$ if $Z_1 = N_2$ and $Z_2 = N_1$. $(a)$ What nuclide is a mirror isobar of $_{11}^{23}Na$? $(b)$ Which nuclide out of the two mirror isobars has greater binding energy and why?

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

The atomic mass of ${ }_7 N ^{15}$ is $15.000108 \text{ a.m.u.}$ and that of ${ }_8 O ^{16}$ is $15.994915 \text{ a.m.u.}$ If the mass of a proton is $1.007825 \text{ a.m.u.}$,then the minimum energy required to remove the least tightly bound proton is ......... $MeV$.