A nucleus with atomic number Z and mass number A has an electrostatic potential V₀ at its surface. If a second nucleus has an atomic number 2Z and a mass number 8A , what is the electrostatic potential at the surface of the second nucleus? (Assume both nuclei are uniformly charged spheres)

Step-by-step solution

The electrostatic potential at the surface of a spherical nucleus of charge Ze and radius R is given by: V₀ = 1 4 ₀ Ze R The radius of a nucleus depends on its mass number A as R = R₀ A^ 1/3 . For the second nucleus, the mass number is 8A . Its radius R' is: R' = R₀ (8A)^ 1/3 = 2 R₀ A^ 1/3 = 2R The charge of the second nucleus is 2Ze (since its atomic number is 2Z ). The electrostatic potential V' at its surface is: V' = 1 4 ₀ 2Ze R' = 1 4 ₀ 2Ze 2R = 1 4 ₀ Ze R = V₀ Answer: V₀