Properties of the nuclear and electrical forces between neutrons and protons. (a) The nuclear force, FN , is the same for a proton and a proton, a neutron and a neutron, or a proton and a neutron.The electrical force only acts between the proton and the proton.The magnitude of the electrical force is the same as that between a proton and an electron. (b) How the forces vary with distance. As the two protons are brought closer together, the electric repulsion becomes stronger, but the nuclear attraction becomes stronger faster.

keep the protons farther apart.) This explains why a nucleus needs approximately as many neutrons as protons.

9.2.2 Binding energy

Since the nuclear force is attractive, we must do work to move two nucleons apart. The work required to disassemble a nucleus is the binding energy of the nucleus (Fig. 9.3). The binding energy is analogous to the binding energy of an atom - the energy required to separate an electron from the rest of the atom, doing work against the electrical attraction. Since the nuclear force is so strong, nuclear binding energies are greater than atomic binding energies by a factor of about 106. We measure nuclear binding energies in MeV, rather than eV. The greater the binding energy of a nucleus, the more work we must do to get the nucleus apart. Therefore, a larger binding energy means a more stable nucleus.

The binding energies of nuclei are so large that we can measure them directly by comparing the mass of a nucleus with the masses of its components. This follows from Einstein's relationship between mass and energy (E = mc2) and conservation of energy

MnucieusC2 + BE = Zmpc2 + Nmnc2

opposed to the electromagnetic and gravitational forces that can be felt at very large distances. For example, we look at the force between two protons. When they are far apart, the electric force dominates, and the protons repel each other. When they are close together, the attractive nuclear force dominates. The strong nuclear force between two protons is the same as between two neutrons and is the same as between a neutron and a proton (Fig. 9.2).

This gives us an idea of the role of a neutron in a nucleus. If we just have protons, the electric repulsion will be appreciable, and the nucleus will not be stable. If we add neutrons, we have additional binding from the nuclear force but no additional electrical repulsion. (The electric repulsion is actually reduced, since the neutrons

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