Two spherical nuclei have mass numbers A₁ and A₂ such that their ratio is A₁ : A₂ = 27 : 125 . What are the ratio of their nuclear densities and the ratio of their nuclear surface areas, respectively?

Step-by-step solution

The density of a nucleus is independent of its mass number. Therefore, the ratio of the nuclear densities is 1 : 1 . The radius of a nucleus is related to its mass number A as R = R₀ A^ 1/3 . The ratio of their radii is R₁ R₂ = ( A₁ A₂ )^ 1/3 = ( 27 125 )^ 1/3 = 3 5 . The surface area of a spherical nucleus is proportional to the square of its radius ( S R^2 ). The ratio of their surface areas is S₁ S₂ = ( R₁ R₂ )^2 = ( 3 5 )^2 = 9 25 . Answer: 1 : 1 and 9 : 25