There is no strict limit to the number of times an atom can undergo nuclear decay. Nuclear decay refers to the process in which an unstable nucleus spontaneously transforms into a more stable configuration by emitting particles or radiation. Different isotopes have different decay modes, such as alpha decay, beta decay, or gamma decay.
In many cases, the decay process continues until a stable nucleus is reached. For example, uranium-238 undergoes a series of radioactive decays, eventually resulting in the formation of a stable lead-206 nucleus after multiple decay steps. This process involves multiple decay events, and there is no inherent limit to the number of decay events that can occur.
However, it's worth noting that the half-life of a radioactive isotope determines the average time it takes for half of a sample to decay. As the number of remaining radioactive atoms decreases over time, the rate of decay also decreases. Eventually, the number of remaining radioactive atoms becomes very small, and the decay process becomes negligible from a practical standpoint.
Additionally, some isotopes have extremely long half-lives, on the order of billions or even trillions of years. For example, uranium-238 has a half-life of about 4.5 billion years. In such cases, the decay process is extremely slow, and it would take an enormous amount of time for a significant fraction of the atoms to decay.
In summary, there is no theoretical limit to the number of times an atom can undergo nuclear decay, but practical considerations such as the half-life of the isotope and the time scales involved can make the decay process negligible in certain cases.