Two spherical nuclei have surface areas in the ratio 16 : 9 . If the mass number of the smaller nucleus is 54 , the mass number of the larger nucleus is _______.

Step-by-step solution

The radius of a nucleus is related to its mass number A by R = R₀ A^ 1/3 . The surface area S of a spherical nucleus is 4 R^2 , so S R^2 A^ 2/3 . Given the ratio of surface areas is S₁ S₂ = 16 9 , we have: ( A₁ A₂ )^ 2/3 = 16 9 Raising both sides to the power of 3 2 : A₁ A₂ = ( 16 9 )^ 3/2 = ( 4 3 )^3 = 64 27 Since the smaller nucleus has mass number A₂ = 54 , the mass number of the larger nucleus is: A₁ = 54 64 27 = 128 Answer: 128