If $M$ is the atomic mass and $A$ is the mass number,the packing fraction is given by

From the given data,the amount of energy required to break the nucleus of aluminium ${ }_{13}^{27} {Al}$ is $x \times 10^{-3} {J}$.
Mass of neutron $= 1.00866 \, {u}$
Mass of proton $= 1.00726 \, {u}$
Mass of aluminium nucleus $= 26.98154 \, {u}$
(Assume $1 \, {u}$ corresponds to $1 \, {J}$ of energy for the purpose of this calculation)
(Round off to the nearest integer)

What is the order of binding energy per nucleon?

List-$I$ shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-$II$. Choose the option that describes the correct match between the entries in List-$I$ to those in List-$II$.

List-$I$	List-$II$
$(P) \ E \propto Z^2$	$(1)$ energy of characteristic $x-$rays
$(Q) \ E \propto (Z-1)^2$	$(2)$ electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range $30$ to $170$
$(R) \ E \propto Z(Z-1)$	$(3)$ energy of continuous $x-$rays
$(S) \ E$ is practically independent of $Z$	$(4)$ average nuclear binding energy per nucleon for stable nuclei with mass number in the range $30$ to $170$
	$(5)$ energy of radiation due to electronic transitions from hydrogen-like atoms

The energy equivalent of $1 \text{ kg}$ of matter is about

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 $2.2 \text{ MeV}$.