What is the band of stability, and why do radioactive isotopes appear on it?

The band of stability, also known as the "valley of stability" or the "line of stable nuclides," is a region in the chart representing isotopes of the elements. In this region, all isotopes are considered stable or non-radioactive due to the balance between the attractive and repulsive forces among the nucleons (protons and neutrons) in their nucleus. Nuclei within the band of stability have the most stable neutron-to-proton (N/Z) ratios, making them energetically stable and less likely to undergo radioactive decay.

Nucleons have two main forces within the nucleus: the attractive strong nuclear force and the repulsive electromagnetic force between protons. The strong nuclear force binds protons and neutrons together, keeping a nucleus intact, while the repulsive electromagnetic force between the protons tends to push them apart due to their positive charges. For a nucleus to be stable, these two forces must counterbalance each other.

The neutron-to-proton (N/Z) ratio is an essential factor in the stability of a nucleus. For lighter elements (atomic number Z ≤ 20), the N/Z ratio is nearly equal to 1, meaning there are roughly the same number of protons and neutrons. This balance helps to maintain stability within the nucleus. As the atomic number Z increases, the N/Z ratio also increases and more neutrons are required to maintain stability. This is because additional neutrons contribute to the strong nuclear force without adding any extra repulsive electromagnetic force, keeping the nucleus stable.

Radioactive isotopes, also known as radionuclides, are nuclei that have unstable N/Z ratios and are prone to undergoing radioactive decay to reach a stable state. They appear outside of the band of stability because their N/Z ratios do not provide stability in their current configuration. As a result, these isotopes have excess energy, which is released during radioactive decay processes, such as alpha, beta, and gamma decay. The radioactive decay helps these isotopes move toward or along the band of stability until they reach a more stable nucleus configuration. In conclusion, the band of stability is a region where isotopes have a balanced N/Z ratio and energetically stable nucleus, while radioactive isotopes appear outside of this region due to their unstable N/Z ratios. These radioactive isotopes undergo radioactive decay to reach a more stable state, thus moving closer to the band of stability.