Show that the volume of a nucleus is proportional to its atomic mass number $A$.

(N/A) The radius $R$ of a nucleus with mass number $A$ is given by the empirical relation: $R = R_0 A^{1/3}$,where $R_0$ is a constant approximately equal to $1.2 \times 10^{-15} \ m$.
The volume $V$ of a nucleus,assuming it is spherical,is given by the formula: $V = \frac{4}{3} \pi R^3$.
Substituting the expression for $R$ into the volume formula:
$V = \frac{4}{3} \pi (R_0 A^{1/3})^3$
$V = \frac{4}{3} \pi R_0^3 A$.
Since $\frac{4}{3}$,$\pi$,and $R_0^3$ are constants,we can write:
$V \propto A$.
Thus,the volume of the nucleus is directly proportional to its atomic mass number $A$.