Nuclear Stability

  February 02, 2022   Read time 3 min
Nuclear Stability
One of the most puzzling questions in nuclear physics is what keeps the nucleus from flying apart. According to the well-established laws of electrostatics, when we bring two positive charges as close together as they are in the nucleus, we expect to encounter a very strong repulsive electrostatic​​​​​​​ force.
The protons should hurl themselves away from each other, ripping the nucleus apart. Scientists provide an answer by postulating that at distances on the order of 10−15 m or less a different fundamental force of nature, the strong nuclear force, takes over. This extremely powerful, but very short-range, attractive force is responsible for holding the nucleons (protons and neutrons) together within the nucleus. Today, physicists understand many features of the strong nuclear force. For example, it is almost independent of electric charge. This means that at a given separation distance (typically, about 10−15 m or less) within the atomic nucleus, the attractive force between two protons, two neutrons, or a proton and a neutron, has nearly the same value.
As the number of nucleons in a nucleus increases, the very limited range of the strong nuclear force also influences its stability in a different manner. To maintain stability in a given nucleus, the attraction between nucleons due to the strong nuclear force must balance the electrostatic repulsion between protons. Because the electrostatic force exerts influence over a very large distance, an individual proton actually interacts with and repels all other protons in a nucleus. However, because of the extremely short range of the strong nuclear force, a proton or neutron attracts only its nearest neighbors. Therefore, as the number of protons (Z) in the nucleus increases, the number of neutrons (N), must increase even more to maintain stability. Figure 4.7 is a very important graph of neutron numbers (N) versus proton numbers (Z) that displays the naturally occurring elements that have stable nuclei. As you can see, there are more neutrons than protons in the nuclides with an atomic number (Z) greater than 20—that is, for the atoms beyond calcium (Ca) in the periodic table. The condition N = Z appears in the figure as a reference line. It corresponds to the condition in which a stable nucleus has the same number of protons as neutrons. Examples of stable nuclides that lie on this reference line include deuterium (2 1H), helium-4 (4 2He), carbon-12 (12 6C), nitrogen-14 (14 7N), and calcium-40 (40 20Ca). Beyond calcium (Z = 20), the points representing the stable nuclei in Figure 4.7 lie above the N = Z reference stability line. This clearly indicates that as the number of protons (Z) increases, additional neutrons are needed to maintain the stability of heavier nuclei. These extra neutrons act like a nuclear glue that holds heavier nuclei together by compensating for the repulsive electrostatic force between protons.
The process of adding neutrons to the nucleus to achieve stability does not continue indefinitely. Eventually, the limited range of the strong nuclear force prevents additional neutrons from balancing the electrostatic repulsion force due to a growing number of protons in the nucleus. Bismuth-209 (209 83Bi) is the stable nucleus with the largest number of protons (Z = 83). All nuclei with an atomic number (Z) greater than 83 are inherently unstable and as time passes spontaneously rearrange their internal structures or break apart. Scientists call this random disintegration process radioactivity. Even for nuclei below Z = 83, only certain combinations of neutrons and protons result in stable nuclei. Isotopes of an element have the same atomic number (Z) but different numbers of neutrons (N). Radioactive isotopes are those nuclides with either too few or too many neutrons for a given number of protons. Radioactivity is discussed in detail later in this chapter. For now, it is sufficient to appreciate that very complex relationships between the nucleons in a nucleus control its stability.

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