Proton Energy in a Nucleus the radii of atomic nuclei are of the order of 5.0 x l0-l5 m.
(a) Estimate the minimum uncertainty in the momentum of a proton if it is confined within a nucleus.
(b) Take this uncertainty in momentum to be an estimate of the magnitude of the momentum. Use the relativistic relationship between energy and momentum, Eq. (37.39), to obtain an estimate of the kinetic energy of a proton confined within a nucleus.
(c) For a proton to remain bound within a nucleus, what must the magnitude of the (negative) potential energy for a proton be within the nucleus? Give your answer in e V and in MeV. Compare to the potential energy for an electron in a hydrogen atom, which has a magnitude of a few tens of e V. (This shows why the interaction that binds the nucleus together is called the "strong nuclear force.")