In the following nuclear reaction,the value of $X$ is: $_7N^{14} + _2He^4 \to X + _1H^1$

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

$A$ nucleus disintegrates into two nuclear parts,in such a way that the ratio of their nuclear radii is $1: 2^{1/3}$. Their respective speeds have a ratio of $n: 1$. The value of $n$ is $.....$.

If the radius of a nucleus with mass number $125$ is $1.5 \text{ fermi}$, then the radius of a nucleus with mass number $64$ is: (in $\text{ fermi}$)

$(a)$ Two stable isotopes of lithium $_{3}^{6} Li$ and $_{3}^{7} Li$ have respective abundances of $7.5 \%$ and $92.5 \%$. These isotopes have masses $6.01512 \; u$ and $7.01600 \; u$,respectively. Find the atomic mass of lithium.
$(b)$ Boron has two stable isotopes,$_{5}^{10} B$ and $_{5}^{11} B$. Their respective masses are $10.01294 \; u$ and $11.00931 \; u$,and the atomic mass of boron is $10.811 \; u$. Find the abundances of $_{5}^{10} B$ and $_{5}^{11} B$.

If $S$ is the surface area of a nucleus of mass number $A$, then