Two nuclei have their mass numbers in the ratio of 1: 3 . The ratio...

Density of nuclear matter is independent of mass number, so the required ratio is $1: 1$. Alternative : $A_1: A_2=1: 3$ Their radii will be in the ratio $\begin{gathered} R_0 A_1^{1 / 3}: R_0 A_2^{1 / 3}=1: 3^{1 / 3} \\ \text{ Density }=\frac{A}{\frac{4}{3} \pi R^3} \\ \therefore \rho_{A_1}: \rho_{A_2}=\frac{1}{\frac{4}{3} \pi R_0^3 \cdot 1^3}: \frac{3}{\frac{4}{3} \pi R_0^3\left(3^{1 / 3}\right)^3} \end{gathered}$ Their nuclear densities will be the same.