Nucleus $A$ having $Z=17$ and an equal number of protons and neutrons has $1.2 \, MeV$ binding energy per nucleon. Another nucleus $B$ of $Z=12$ has a total of $26$ nucleons and $1.8 \, MeV$ binding energy per nucleon. The difference in binding energy of $B$ and $A$ will be $........... \, MeV$.

The mass of ${ }_7 N ^{15}$ is $15.00011 \ amu$,the mass of ${ }_8 O ^{16}$ is $15.99492 \ amu$,and $m_p = 1.00783 \ amu$. Determine the binding energy of the last proton of ${ }_8 O ^{16}$ in $MeV$.

$A$ given coin has a mass of $3.0\; g$. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity, assume that the coin is entirely made of $_{29}^{63} Cu$ atoms (of mass $62.92960\; u$).

Binding energy per nucleon of a fixed nucleus $X^A$ is $8 \ MeV$. It absorbs a neutron moving with kinetic energy $2 \ MeV$ and converts into $Y$,emitting two photons of energy $1 \ MeV$ and $4 \ MeV$ respectively one after the other. The binding energy per nucleon of $Y$ (in $MeV$) is:

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.

In a nuclear reaction,which of the following is conserved?