Consider two bare nuclei of isotopes of a single element, having mass numbers 64 and 125 respectively. The ratio of the electrostatic potentials at their nuclear surfaces is:

Step-by-step solution

Since the two nuclei are isotopes of the same element, they have the same atomic number Z . Thus, the total charge on both bare nuclei is identical, Q = +Ze . The electrostatic potential V at the surface of a spherical nucleus of radius R and charge Q is given by V = 1 4 ₀ Q R . Because Q is constant for both isotopes, the potential is inversely proportional to the nuclear radius: V 1 R . The nuclear radius depends on the mass number A as R = R₀ A^ 1/3 . Therefore, V A^ -1/3 . For the two isotopes with mass numbers