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 ........... $MeV$.

The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by $E = \frac{3}{5} \frac{Z(Z-1) e^2}{4 \pi \varepsilon_0 R}$. The measured masses of the neutron,${ }_1^1 H$,${ }_7^{15} N$,and ${ }_8^{15} O$ are $1.008665 \ u$,$1.007825 \ u$,$15.000109 \ u$,and $15.003065 \ u$,respectively. Given that the radii of both the ${ }_7^{15} N$ and ${ }_8^{15} O$ nuclei are the same,$1 \ u = 931.5 \ MeV/c^2$ ($c$ is the speed of light),and $e^2 / (4 \pi \varepsilon_0) = 1.44 \ MeV \ fm$. Assuming that the difference between the binding energies of ${ }_7^{15} N$ and ${ }_8^{15} O$ is purely due to the electrostatic energy,the radius of either of the nuclei is $(1 \ fm = 10^{-15} \ m)$: (in $fm$)

Given below are two statements:
Statement $I$: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement $II$: For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below:

Binding energy of a certain nucleus is $18 \times 10^8 \ J$. How much is the difference between the total mass of all the nucleons and the nuclear mass of the given nucleus (in $\mu g$)?

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, what is the energy released in $MeV$?

In nuclear reactions,which of the following quantities are conserved?