Two protons are kept at a separation of $10 \ nm$. Let $F_n$ and $F_e$ be the nuclear force and the electromagnetic force between them,respectively.

Consider the following statements ($X$ and $Y$ stand for two different elements):
$(I)$ ${ }_{32}^{65} X$ and ${ }_{33}^{65} Y$ are isotopes.
$(II)$ ${ }_{42}^{86} X$ and ${ }_{42}^{85} Y$ are isotopes.
$(III)$ ${ }_{85}^{174} X$ and ${ }_{88}^{177} Y$ have the same number of neutrons.
$(IV)$ ${ }_{92}^{235} X$ and ${ }_{94}^{235} Y$ are isobars.
Which of the above statements are correct?

$A$ heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $8 : 1$. Find the ratio of the radii of the fragments.

In the nuclear reaction $X(n, \alpha) _3^7Li$,what is $X$?

Are the nucleons fundamental particles,or do they consist of still smaller parts? One way to find out is to probe a nucleon just as Rutherford probed an atom. What should be the kinetic energy of an electron for it to be able to probe a nucleon? Assume the diameter of a nucleon to be approximately $10^{-15} \ m$.

The distance between two nucleons for which the potential energy is minimum,is (in $fm$)