Question

A nucleus has mass number $A_1$ and volume $V_1$. Another nucleus has mass number $A_2$ and volume $V_2$. If the relation between mass numbers is $A_2 = 4A_1$, then $\frac{V_2}{V_1} =$ _______.

Answer 1

For a nucleus, the volume $V$ is proportional to $A$, the mass number, given by:

$V = \frac{4}{3}\pi R^3,$

where the radius $R$ of a nucleus is proportional to the cube root of its mass number $A$:

$R = R_0 A^{1/3}.$

Thus, the volume $V$ of a nucleus can be expressed as:

$V \propto A.$

Since $A_2 = 4A_1$, the ratio of volumes is:

$\frac{V_2}{V_1} = \frac{A_2}{A_1} = 4.$