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

Which of the following is most unstable?

The ratio of the density of oxygen nucleus $\left({ }_{8}^{16} O \right)$ and helium nucleus $\left({ }_{2}^{4} He \right)$ is (in $:1$)

If the nuclear forces between two protons,two neutrons,and a proton-neutron are denoted by $F_{pp}$,$F_{nn}$,and $F_{pn}$ respectively,then:

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

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?