Two spherical nuclei have mass numbers 8 and 125 respectively. The ratio of their nuclear surface areas is:

Step-by-step solution

The radius of a nucleus is related to its mass number A by the formula R = R₀ A^ 1/3 . The surface area S of a spherical nucleus is given by S = 4 R^2 . Therefore, the surface area is proportional to the square of the radius: S R^2 (A^ 1/3 )^2 = A^ 2/3 . For the two nuclei with mass numbers A₁ = 8 and A₂ = 125 , the ratio of their surface areas is: S₁ S₂ = ( A₁ A₂ )^ 2/3 = ( 8 125 )^ 2/3 S₁ S₂ = ( ( 2 5 )^3 )^ 2/3 = ( 2 5 )^2 = 4 25 Thus, the required ratio is 4 : 25 . Answer: 4 : 25