Answer to Question #145926 in Atomic and Nuclear Physics for Arsam

Question

Why the number of neutrons tends to exceed the number of protons in stable nuclei?

Answer 1

For nuclei with higher atomic numbers, the number of neutrons exceeds the number of protons. Indeed, the number of neutrons necessary to create a stable nucleus increases more rapidly than the number of protons, as shown in picture. This is connected with semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula) that explains main (but far not all!) nuclear properties connected with the binding energy. Protons feel repulsion via Coulomb forces, but the nuclear forces that act on both protons and neutrons keep the nuclei in bounded state. So if protons bring both interaction and repulsion, the neutrons contribute only to the bounding of nuclei. Also with the increase of A, the nuclei becomes larger. However, strong interaction is short-range interaction, so you need more particles to "glue" the nucleus together, but not the charged ones. All these effects are taken into account in Weizsäcker formula that predicts stability zone for nuclei.

However, if we take the nuclei with too high neutron-to-proton ratio, it appears that this configuration is not energetically beneficial in comparison with neutron-to-proton ratio from the belt of stability. In this case, nuclei move toward the belt of stability by emitting a beta particle.