The radius of a nucleus of a mass number $A$ is directly proportional to

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?

Calculate the height of the potential barrier for a head-on collision of two deuterons. (Radius of deuteron is $2$ fm).

What is the ratio of the radii of the nuclei $_{13}^{27}Al$ and $_{52}^{125}Te$?

The ratio of the nuclear radii of the gold isotope ${}_{79}^{197}Au$ and the silver isotope ${}_{47}^{107}Ag$ is $ . . . . . . $.

On the bombardment of a neutron with Boron,an $\alpha$-particle is emitted. The product nucleus formed is: