In the nuclear reaction $_2He^4 + _zX^A \to _{z+2}Y^{A+3} + A$,$A$ denotes:

State the dimension of the nucleus from the Rutherford experiment.

Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be

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

Given below are three schematic graphs of potential energy $V(r)$ versus distance $r$ for three atomic particles: electron $(e^{-})$,proton $(p^{+})$,and neutron $(n)$,in the presence of a nucleus at the origin $O$. The radius of the nucleus is $r_0$. The scale on the $V$-axis may not be the same for all figures. The correct pairing of each graph with the corresponding atomic particle is

The ratio of the volume of an $Al^{27}$ nucleus to its surface area is (Given,$R_0 = 1.2 \times 10^{-15} \ m$):