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(B) The radius of a nucleus is given by $R = R_0 A^{1/3}$,where $A$ is the mass number and $R_0$ is a constant.The volume of a nucleus is $V = \frac{4

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$1 : 1$

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(B) The radius of a nucleus is given by $R = R_0 A^{1/3}$,where $A$ is the mass number and $R_0$ is a constant.The volume of a nucleus is $V = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A$.The nuclear density $\rho$ is defined as the ratio of mass to volume: $\rho = \frac{M}{V} = \frac{A \cdot m_p}{\frac{4}{3} \pi R_0^3 A}$,where $m_p$ is the average mass of a nucleon.Since $A$ cancels out,$\rho = \frac{m_p}{\frac{4}{3} \pi R_0^3}$.This shows that the nuclear density is independent of the mass number $A$.Therefore,the ratio of the nuclear densities of any two nuclei is always $1 : 1$.

Two nuclei have their mass numbers in the ratio of $1 : 3.$ The ratio of their nuclear densities would be

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