Before the discovery of the neutron, one theory of the nucleus proposed that the nucleus contains protons and electrons. For example, the helium-4 nucleus would contain 4 protons and 2 electrons instead of-as we now know to be true-2 protons and 2 neutrons.
(a) Assuming that the electron moves at nonrelativistic speeds, find the ground-state energy in mega-electronvolts of an electron confined to a one-dimensional box of length 5.0 fm (the approximate diameter of the 4 He nucleus). (The electron actually does move at relativistic speeds. See Problem 80.)
(b) What can you conclude about the electron-proton model of the nucleus? The binding energy of the 4 He nucleus-the energy that would have to be supplied to break the nucleus into its constituent particles-is about 28 MeV.
(c) Repeat (a) for a neutron confined to the nucleus (instead of an electron). Compare your result with (a) and comment on the viability of the proton-neutron theory relative to the electron-proton theory.