The ratio of the nuclear radii of two nuclei X and Y is 1:3 . What are the ratio of their mass numbers and the ratio of their nuclear mass densities, respectively?

Step-by-step solution

The radius of a nucleus R is related to its mass number A by R = R₀ A^ 1/3 . Given the ratio of radii R_X R_Y = 1 3 , we can write: ( A_X A_Y )^ 1/3 = 1 3 Cubing both sides gives the ratio of their mass numbers: A_X A_Y = ( 1 3 )^3 = 1 27 The nuclear mass density is given by = Mass Volume m A 4 3 R₀^3 A = 3m 4 R₀^3 . Since the density is independent of the mass number A , it is approximately constant for all nuclei. Therefore, the ratio of their nuclear mass densities is 1:1 . The required ratios are 1:27 and 1:1 .