NEETPhysicsNuclear Physics
Match List-I with List-II regarding the dependence of various nuclear properties on the mass number A . List-I List-II (A) Nuclear Radius (I) Proportional to A^0 (B) Nuclear Volume (II) Proportional to A^ 1/3 (C) Nuclear Density (III) Proportional to A^1 (D) Nuclear Surface Area (IV) Proportional to A^ 2/3 Choose the correct answer from the options given below:
Options
- A(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
- B(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
- C(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
- D(A)-(II), (B)-(III), (C)-(I), (D)-(IV)
Correct answer
D. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
Step-by-step solution
The radius of a nucleus R depends on its mass number A as R = R₀ A^ 1/3 . Thus, Nuclear Radius is proportional to A^ 1/3 . The volume of a nucleus V = 4 3 R^3 = 4 3 R₀^3 A . Thus, Nuclear Volume is proportional to A^1 . The nuclear density = Mass Volume m A 4 3 R₀^3 A = 3m 4 R₀^3 . Thus, Nuclear Density is independent of A , meaning it is proportional to A^0 . The surface area of a nucleus S = 4 R^2 = 4 R₀^2 A^ 2/3 . Thus, Nuclear Surface Area is proportional to A^ 2/3 . Therefore, the correct matching is (A)-(II),