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(C) The radius of a nucleus is given by $R = R_{0} A^{\frac{1}{3}}$,where $A$ is the mass number and $R_{0}$ is a constant.The density of a nucleus $\

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$1: 1$

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(C) The radius of a nucleus is given by $R = R_{0} A^{\frac{1}{3}}$,where $A$ is the mass number and $R_{0}$ is a constant.The density of a nucleus $ho$ is defined as the ratio of the mass of the nucleus to its volume.$ho = \frac{	ext{Mass of nucleus}}{	ext{Volume of nucleus}} = \frac{m 	imes A}{\frac{4}{3} \pi R^{3}}$,where $m$ is the average mass of a nucleon (proton or neutron).Substituting the expression for $R$:$ho = \frac{m 	imes A}{\frac{4}{3} \pi (R_{0} A^{\frac{1}{3}})^{3}} = \frac{m 	imes A}{\frac{4}{3} \pi R_{0}^{3} A}$.Simplifying the expression,the $A$ terms cancel out:$ho = \frac{m}{\frac{4}{3} \pi R_{0}^{3}}$.Since $ho$ is independent of the mass number $A$,the nuclear density is constant for all nuclei.Therefore,the ratio of the nuclear densities of two nuclei is $1: 1$.

Mass numbers of two nuclei are in the ratio of $4: 3$. Their nuclear densities will be in the ratio of

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