The ratio of nuclear densities of two nuclei having mass numbers A an…

The correct answer is Option (2) → 1 : 1

Density of a nucleus: $\rho = \frac{\text{Mass}}{\text{Volume}}$

Mass of nucleus $\propto A$, Volume of nucleus $\propto R^3 \propto A$ (since $R \propto A^{1/3}$)

So, $\rho \propto \frac{A}{(A^{1/3})^3} = \frac{A}{A} = 1$

For two nuclei with mass numbers $A$ and $8A$, their densities:

$\rho_1 / \rho_2 = 1$

Ratio of nuclear densities = 1 : 1