Match List-I with List-II regarding the dependence of various...

The radius of a nucleus $R$ depends on its mass number $A$ as $R = R_0 A^{1/3}$. Thus, Nuclear Radius is proportional to $A^{1/3}$.

The volume of a nucleus $V = \dfrac{4}{3}\pi R^3 = \dfrac{4}{3}\pi R_0^3 A$. Thus, Nuclear Volume is proportional to $A^1$.

The nuclear density $\rho = \dfrac{\text{Mass}}{\text{Volume}} \approx \dfrac{m A}{\dfrac{4}{3}\pi R_0^3 A} = \dfrac{3m}{4\pi R_0^3}$. Thus, Nuclear Density is independent of $A$, meaning it is proportional to $A^0$.

The surface area of a nucleus $S = 4\pi R^2 = 4\pi R_0^2 A^{2/3}$. Thus, Nuclear Surface Area is proportional to $A^{2/3}$.

Therefore, the correct matching is (A)-(II), (B)-(III), (C)-(I), (D)-(IV).

Answer: (A)-(II), (B)-(III), (C)-(I), (D)-(IV)