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How much energy is released when a \( { }^{238} \mathrm{U} \) nucleus decays by emitting (a) an alpha particle and (b) a sequence of neutron, proton, neutron, proton? (c) Convince yourself both by reasoned argument and by direct calculation that the difference between these two numbers is just the total binding energy of the alpha particle. (d) Find that binding energy. Some needed atomic and particle masses are
\( \begin{array}{lllr}{ }^{238} \mathrm{U} & 238.05079 \mathrm{u} & { }^{23} \mathrm{Th} & 234.04363 \mathrm{u} \\ { }^{237} \mathrm{U} & 237.04873 \mathrm{u} & { }^{4} \mathrm{He} & 4.00260 \mathrm{u} \\ { }^{236} \mathrm{~Pa} & 236.04891 \mathrm{u} & { }^{1} \mathrm{H} & 1.00783 \mathrm{u} \\ { }^{235} \mathrm{~Pa} & 235.04544 \mathrm{u} & \mathrm{n} & 1.00866 \mathrm{u}\end{array} \)
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