The energy equivalent to a mass of $1 \,kg$ is

What is the energy produced in $MeV$ when the mass equivalent to $1$ proton is completely converted into energy?

The radionuclide $^{11}_{6}C$ decays by $\beta^+$ emission. Given that $m(^{11}_{6}C) = 11.011434 \ u$,$m(^{11}_{5}B) = 11.009305 \ u$,$m_e = 0.000548 \ u$,and $1 \ u = 931.5 \ MeV/c^2$. The $Q$-value of this decay process is:

An electron and a positron annihilate each other to produce two $\gamma$-ray photons of equal energy. The minimum energy of each photon is .....

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

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 $fm$)