The ratio of the density of oxygen nucleus le | vedclass

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(C) The nuclear density is defined as the ratio of the mass of the nucleus to its volume.Let $A$ be the mass number and $R$ be the radius of the nucle

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$1$

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(C) The nuclear density is defined as the ratio of the mass of the nucleus to its volume.Let $A$ be the mass number and $R$ be the radius of the nucleus.The radius of a nucleus is given by $R = R_0 A^{1/3}$,where $R_0$ is a constant.The volume of the 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 mass of the nucleus is approximately $M = A \cdot u$,where $u$ is the atomic mass unit.Therefore,the nuclear density $\rho = \frac{M}{V} = \frac{A \cdot u}{\frac{4}{3} \pi R_0^3 A} = \frac{3u}{4 \pi R_0^3}$.Since the expression for nuclear density depends only on constants ($u$ and $R_0$),it is independent of the mass number $A$.Thus,the density of all nuclei is the same.Therefore,the ratio of the density of oxygen nucleus to helium nucleus is $1:1$.

The ratio of the density of oxygen nucleus $\left({ }_{8}^{16} O \right)$ and helium nucleus $\left({ }_{2}^{4} He \right)$ is (in $:1$)

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