Two nuclei have their mass numbers in the rat | vedclass

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(D) The nuclear density $\rho$ is defined as the ratio of the mass of the nucleus to its volume. Since the mass of a nucleus is approximately $M = A \

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$1: 1$

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(D) The nuclear density $\rho$ is defined as the ratio of the mass of the nucleus to its volume. Since the mass of a nucleus is approximately $M = A \cdot m_p$ (where $A$ is the mass number and $m_p$ is the mass of a nucleon) and the volume is $V = \frac{4}{3} \pi R^3$,where $R = R_0 A^{1/3}$. Substituting the expression for $R$,we get $V = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A$. Thus,$\rho = \frac{A \cdot m_p}{\frac{4}{3} \pi R_0^3 A} = \frac{m_p}{\frac{4}{3} \pi R_0^3}$. This expression 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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