A nucleus of mass number 27 has a radius R . If another nucleus has a radius of 2R , its mass number will be:

Step-by-step solution

The radius of a nucleus R is related to its mass number A by the relation: R = R₀A^ 1 3 For the first nucleus: R₁ = R = R₀(27)^ 1 3 For the second nucleus: R₂ = 2R = R₀(A₂)^ 1 3 Taking the ratio of the two radii: R₂ R₁ = ( A₂ 27 )^ 1 3 2 = ( A₂ 27 )^ 1 3 Cubing both sides, we get: 8 = A₂ 27 A₂ = 27 8 = 216 Answer: 216