A nucleus (of nuclear density rho) disintegra | vedclass

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(D) Nuclear density is defined as the ratio of the mass of the nucleus to its volume.The volume $V$ of a nucleus with mass number $A$ is given by $V =

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$\rho$

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(D) Nuclear density is defined as the ratio of the mass of the nucleus to its volume.The volume $V$ of a nucleus with mass number $A$ is given by $V = \frac{4}{3} \pi R^3$,where $R = R_0 A^{1/3}$.Thus,$V = \frac{4}{3} \pi R_0^3 A$.The density $\rho$ is given by $\rho = \frac{M}{V} = \frac{A \cdot m_p}{\frac{4}{3} \pi R_0^3 A} = \frac{3 m_p}{4 \pi R_0^3}$,where $m_p$ is the mass of a nucleon.Since $m_p$,$\pi$,and $R_0$ are constants,the nuclear density $\rho$ is independent of the mass number $A$.Therefore,the density of the daughter nuclei remains the same as the parent nucleus,which is $\rho$.

$A$ nucleus (of nuclear density $\rho$) disintegrates into two daughter nuclei with masses in the ratio $8 : 27$. The density of the smaller nucleus is

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