Choose the correct statements from the following based on the properties of atomic nucleus.

I. Radius of a nucleus of man no. A depends on its mass number as $R \propto A^3$
II. Radius of nucleus and mass number are related as $R \propto A^{\frac{1}{3}}$
III. Density of nuclei is always a constant
IV. Density of nuclei depends on its mass number A
V. Density of nuclei depends on its size, volume

Choose the correct answer from the options given below:

II and III only

The correct answer is Option (2) → II and III only

Sol. We known, volume of nucleus $V \propto A$

∴  $\frac{4}{3} \pi R^3 \propto A$

∴  $R \propto A^{1 / 3}$

Now, density of nucleus $\rho=\frac{M}{V}=\frac{A}{\frac{4}{3} \pi\left(R_0 A^{1 / 3}\right)^3}$

$\rho=\frac{1}{\frac{4}{3} \pi R_0^3} \Rightarrow$ constant

Thus density of nucleus is constant