A shorter half-life indicates what about a nucleus?

A shorter half-life is indicative of a nucleus that is likely to decay more quickly. The half-life of a radioactive isotope represents the time it takes for half of a sample to undergo decay. When this time is short, it means that the isotope is less stable and will undergo radioactive decay at a faster rate.

In the context of nuclear stability, isotopes with shorter half-lives tend to be those that are unstable and possess a higher probability of undergoing decay processes, such as alpha or beta decay. This rapid decay can be attributed to factors such as strong nuclear forces weakening or an imbalance in the number of protons and neutrons, leading to instability.

Thus, a nucleus with a shorter half-life indeed suggests that it will decay more rapidly compared to those with longer half-lives, which are associated with greater stability and slower decay rates.