1. The neutron-to-proton ratio (n/p), the most stable ratio being that indicated by the stability curve
2. Pairing of nucleons as indicated by the even-odd rules
3. The binding energy, which is related to the mass defect and the packing fraction
The Even-Odd Rules
1. There is instability when there is an odd number of neutrons or protons in the nucleus
2. Of the 300 stable nuclides, about 200 have both an even number of protons and neutrons.
3. Only 4 stable nuclides exist having both an odd number of protons and neutrons, e.g., deuterium =H11
Neutron/Proton Ratio Graph
1. If one plots the # of neutrons in the nucleus of a particular radionuclide vs the number of protons for the same nuclide for all three thousand known nuclides, the graph above will be obtained. The yellow band represents the “band of stability” and its edges are not as smooth as in the diagram. Any nuclide falling in the band of stability will be stable and therefore not radioactive.
2. Only about 8% of all known nuclides are stable; the remainder plot in a region above the curve known as the “neutron excessive region” or a region below the curve known as the “neutron deficient region”.
3. If a nuclide plots in the “neutron excessive region” represented by point A in the diagram, the implication is that it has too many neutrons per proton and, as reflected in the diagram, must lose a neutron and gain a proton to decrease the ratio and achieve stability. On the other hand, if a nuclide plots in the “neutron deficient region” represented by point B in the diagram, the implication is that it has too few neutrons per proton and, as reflected in the diagram, must lose a proton and gain a neutron to increase the ratio and achieve stability.
4. As indicated in the diagram, the curve is not linear but gently curves upward as a function of increased proton number, meaning that to achieve stability, the number of neutrons must increase at a somewhat greater rate than the number of protons. For example, for a Z number of 80, it might require 120 neutrons and 80 protons to achieve stability whereas for a Z number of 10, it would take 10 neutrons and 10 protons to achieve stability. These would represent n/p ratios of 1.5:1.0 and 1:0:1.0, respectively. In reality, the relationship is linear only through Z = 8, after which there are deviations. For example, F-18 has 9 neutrons and 9 protons, with a n/p ratio of 1:0:1.0, but it is radioactive.