19. (a) Since the nuclear force has a short range, any nucleon interacts only with its nearest neighbors,
not with more distant nucleons in the nucleus. Let N be the number of neighbors that interact
with any nucleon. It is independent of the number A of nucleons in the nucleus. The number of
interactions in a nucleus is approximately NA, so the energy associated with the strong nuclear
force is proportional to NA and, therefore, proportional to A itself.
(b) Each proton in a nucleus interacts electrically with every other proton. The number of pairs of
protons is Z(Z - 1)/2, where Z is the number of protons. The Coulomb energy is, therefore,
proportional to Z(Z - 1).
(c) As A increases, Z increases at a slightly slower rate but Z2 increases at a faster rate than A and
the energy associated with Coulomb interactions increases faster than the energy associated with
strong nuclear interactions.
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