What is the band of stability?
The band of stability is a graphical representation of stable nuclei plotted according to their number of protons (Z) and neutrons (N). When neutron number is plotted against proton number, stable nuclei fall within a narrow region or “band.” Nuclei that lie outside this band are unstable and tend to undergo radioactive decay in order to move toward a more stable neutron-to-proton ratio.
The band of stability describes the region of neutron–proton combinations that produce stable nuclei. Isotopes outside this band undergo radioactive decay.
For light elements, stability generally occurs when the number of neutrons is approximately equal to the number of protons. As atomic number increases, however, stable nuclei require progressively more neutrons than protons. This shift reflects the need to counterbalance increasing electrostatic repulsion between protons within the nucleus.
Nuclei that are neutron-rich or proton-rich relative to the band of stability are unstable and will decay via specific mechanisms (such as beta minus decay or positron emission) to restore a more stable configuration.
Understanding the physics
The band of stability arises from the competing forces within the nucleus. The strong nuclear force binds protons and neutrons together but acts only over very short distances. Meanwhile, protons repel each other through electrostatic forces, and this repulsion increases as more protons are packed into the nucleus.
In light nuclei (low Z), the strong nuclear force is sufficient to stabilise nuclei with roughly equal numbers of neutrons and protons. There is relatively little electrostatic repulsion to overcome, so the N/Z ratio is close to 1.
As atomic number increases, the cumulative proton–proton repulsion becomes much more significant. Additional neutrons are required to provide extra strong-force binding without increasing electrostatic repulsion. This causes the band of stability to curve upward, with stable heavy nuclei having substantially more neutrons than protons.
When a nucleus lies outside this band, it is energetically favourable for it to transform. A neutron-rich nucleus can convert a neutron into a proton through beta minus decay, reducing its neutron excess. A proton-rich nucleus can convert a proton into a neutron via positron emission or electron capture. These decay processes move the nucleus diagonally toward the band of stability.
Very heavy nuclei (typically beyond atomic number 83) cannot achieve long-term stability because proton repulsion becomes too strong, even with additional neutrons. As a result, they tend to undergo alpha decay or other decay processes.
Where this matters clinically
The band of stability explains why radionuclides used in nuclear medicine undergo specific decay modes. For example, neutron-rich isotopes commonly used in SPECT imaging decay by beta minus emission, while proton-rich isotopes used in PET imaging undergo positron emission. The position of an isotope relative to the band determines how it decays and therefore how it can be used diagnostically.