A nucleus may be treated as a uniform sphere of radius R containing A nucleons, of which Z are protons.
(i) Assuming each nucleon attracts only a fixed number of nearest neighbours through the nuclear force, show that the total nuclear interaction energy is proportional to A.
(ii) Treat the positive charge as uniformly distributed throughout the sphere. Prove that the total electrostatic potential energy of the protons is proportional to Z2/A1/3.
(iii) Using the results of (i) and (ii), explain why very heavy nuclei with large Z and A become unstable against fission, even though the nuclear force is far stronger than the electrostatic force at short separations.