JEE MainPhysicsNuclear Physics
The ratio of the surface areas of two spherical nuclei is 16 : 9 . The ratio of their mass numbers will be
Options
- A16 : 9
- B64 : 27
- C4 : 3
- D256 : 81
Correct answer
B. 64 : 27
Step-by-step solution
The surface area of a spherical nucleus is S = 4 R^2 , which means S R^2 . Given S₁ S₂ = 16 9 , we can find the ratio of their radii: R₁ R₂ = 16 9 = 4 3 The radius of a nucleus is related to its mass number A by R = R₀ A^ 1/3 , which implies A R^3 . Therefore, the ratio of their mass numbers is: A₁ A₂ = ( R₁ R₂ )^3 = ( 4 3 )^3 = 64 27 Answer: 64 : 27