(a) Energy is required to separate a nucleus into its constituent nucleons, as Interactive Figure 31.3 indicates; this energy is the total binding energy of the nucleus. In a similar way one can speak of the energy that binds a single nucleon to the remainder of the nucleus. For example, separating nitrogen ${ }^{14}{ }_{7} \mathrm{N}$ into nitrogen ${ }^{13}{ }_{7} \mathrm{N}$ and a neutron takes energy equal to the binding energy of the neutron, as shown below: Find the energy (in MeV) that binds the neutron to the ${ }^{14}, \mathrm{N}$ nucleus by considering the mass of ${ }_{7}^{13} \mathrm{N}$ (atomic mass $=13.005738 \mathrm{u}$ ) and the mass of ${ }_{0}^{1}$ n (atomic mass $=1.008665 \mathrm{u}$ ), as compared to the mass of ${ }_{7}^{14} \mathrm{N}$ (atomic mass $=$ $14.003074 \mathrm{u}) .$ (b) Similarly, one can speak of the energy that binds a single proton to the ${ }^{14}{ }_{7} \mathrm{N}$ nucleus: Following the procedure outlined in part (a), determine the energy (in MeV) that binds the proton (atomic mass $=1.007825 \mathrm{u}$ ) to the ${ }_{7}^{14} \mathrm{N}$ nucleus. The atomic mass of carbon ${ }_{6}^{13} \mathrm{C}$ is $13.003355 \mathrm{u}$. (c) Which nucleon is more tightly bound, the neutron or the proton?