Read the following statements:(A) Volume of t | vedclass

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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.The volume $V$ of the nucleus is given by $V = \frac{4}{3} \pi

Vedclass · Accepted Answer

$(A)$ and $(E)$ only.

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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.The volume $V$ of the nucleus is given by $V = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A$.Since $\frac{4}{3} \pi R_0^3$ is a constant,the volume $V$ is directly proportional to the mass number $A$. Thus,statement $(A)$ is correct.The density $ho$ of the nucleus is given by $ho = \frac{	ext{Mass}}{	ext{Volume}} = \frac{m A}{V}$,where $m$ is the average mass of a nucleon.Substituting $V \propto A$,we get $ho = \frac{m A}{k A} = \frac{m}{k}$,where $k$ is a constant.Since $ho$ is a constant,the density of the nucleus is independent of the mass number $A$. Thus,statement $(E)$ is correct.Therefore,statements $(A)$ and $(E)$ are correct.

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