Four statements are given (A is mass number) | vedclass

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(B) The radius of a nucleus is given by $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.The volume of a nucleus is $V = \frac{4

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$B$ and $D$ are true,but $A$ and $C$ are false

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(B) The radius of a nucleus is given by $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.The volume of a nucleus is $V = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A$.Since $\frac{4}{3} \pi R_0^3$ is a constant,the volume $V$ is directly proportional to the mass number $A$. Therefore,statement $A$ is false and statement $B$ is true.Mass defect is defined as the difference between the sum of the masses of the individual nucleons (protons and neutrons) and the actual mass of the nucleus. Therefore,statement $C$ is false and statement $D$ is true.Thus,statements $B$ and $D$ are true,while $A$ and $C$ are false.

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