Physics 222 -- Notes on Chapter 21

Just as the covalent bond comes from residual electric forces between combinations of particles which are electrically neutral (i. e., atoms), the nuclear force is a residual strong force between colorless particles such as protons and neutrons. The binding energies between nucleons (i. e., protons and neutrons) are of order 0.01 times quark binding energies. The nuclear force is short range, attractive at distances greater than about 2e-15 m, and strongly repulsive at shorter distances. Thus, atomic nuclei have sizes of order a few times 2e-15 m.

The binding energy of an atomic nucleus is the rest energy of the protons and neutrons making up the nucleus, minus the rest energy of the fully assembled nucleus.

The amount of energy released or absorbed by various nuclear reactions can be assessed by using the principle of energy conservation.

There is an approximate formula for the binding energy of atomic nuclei. This formula provides a rough approximation to binding energies, but fails badly for nuclei with small numbers of protons and neutrons.

The binding energy formula fails to take into account the energetic effects of closed nuclear shells, which are more stable than nuclei with non-closed shells. In particular, nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. The alpha particle (2 protons plus 2 neutrons) is an example of an exceptionally stable nucleus.

You should know the consequences of the binding energy formula in defining where the most stable nuclei exist in the A-N plane. The various forms of radioactive decay (alpha, beta, gamma) can be explained in terms of the differences in rest energy between different nuclei and the forces at work in each of these decay processes.

Energy-releasing nuclear fusion can occur when nuclei with combined Z less than or equal to that for iron collide. However, large collision velocities are needed to overcome Coulomb repulsion between the nuclei. Energy-releasing nuclear fission can occur when heavy nuclei split into pieces. Fission can be stimulated by a collision between certain heavy nuclei and a neutron. Since fission itself produces free neutrons, a chain reaction can occur, in which fission produces neutrons, which produces more fission, etc. If the fissioning nucleus has an odd number of neutrons, then fission can be induced by very low energy neutrons (Uranium-235, Plutonium-239). If the nucleus has an even number of neutrons, this cannot happen (Uranium-238).