Why do radioactive nuclei decay at unpredictable individual times?

Radioactive nuclei decay at unpredictable individual times because the process is governed by the laws of quantum mechanics, which are inherently probabilistic rather than deterministic.12

While it is impossible to predict exactly when a specific atom will undergo decay, the process follows a constant, predictable rate when observing a large collection of identical nuclei. This behavior is often compared to the statistical predictability of death rates in human populations; while the individual outcome is uncertain, the aggregate behavior is highly consistent.3

For certain types of decay, such as alpha decay, the unpredictability is explained by the phenomenon of quantum tunneling. In this process, a particle confined within a nucleus has a small, calculated probability of "tunneling" through a potential energy barrier to escape, even if it lacks the classical energy to do so. The specific time an individual nucleus decays is a result of this random quantum event, making the timing of any single decay fundamentally unpredictable.14