$A$ nucleus with atomic mass number $A$ produces another nucleus by losing $2$ alpha particles. The volume of the new nucleus is $60$ times that of the alpha particle. The atomic mass number $A$ of the original nucleus is:

$A$ nucleus has mass number $\alpha$ and radius $R_{\alpha}$. Another nucleus has mass number $\beta$ and radius $R_{\beta}$. If $\beta = 8\alpha$, then $R_{\alpha}/R_{\beta}$ is:

Is nuclear force short range or long range?

In the nuclear reaction ${ }_{7}^{14} N + X \rightarrow { }_{6}^{14} C + { }_{1}^{1} H$, the $X$ will be

Nuclei with magic numbers of protons $Z = 2, 8, 20, 28, 50, 82$ and magic numbers of neutrons $N = 2, 8, 20, 28, 50, 82, 126$ are found to be very stable.
$(i)$ Verify this by calculating the proton separation energy $S_p$ for $^{120}Sn$ $(Z = 50)$ and $^{121}Sb$ $(Z = 51)$. The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by $S_p = (M_{Z-1, N} + M_H - M_{Z, N})c^2$. Given:
$^{119}In = 118.9058 \ u, ^{120}Sn = 119.902199 \ u, ^{121}Sb = 120.903824 \ u, ^1H = 1.0078252 \ u$
$(ii)$ What does the existence of magic numbers indicate?

The maximum potential energy due to electrostatic repulsion between two hydrogen nuclei is nearly (radius of the nucleus $= 1.1 \ Fermi$). $\left[ \frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ N \ m^2 \ C^{-2} \right]$ (in $MeV$)