In quantum mechanics, the decay of a radioactive nucleus is considered to be a stochastic or probabilistic process. This means that while we can calculate the average decay rate for a large number of identical nuclei, it is not possible to predict the exact moment when an individual nucleus will decay.
The decay of a radioactive nucleus is described by a mathematical model called exponential decay. This model provides a probability distribution for the decay process, typically characterized by a parameter known as the half-life. The half-life represents the time it takes for half of the radioactive nuclei in a sample to decay.
Given a large number of identical nuclei, we can use the exponential decay model and statistical methods to calculate the decay probability over a certain period. However, for an individual nucleus, the exact moment of decay cannot be determined in advance. It is fundamentally unpredictable.
The probabilistic nature of radioactive decay arises from the inherent randomness of quantum mechanics. Quantum processes, such as nuclear decay, are subject to inherent uncertainties and fluctuations at the microscopic level, making the prediction of individual decay events impossible.
Therefore, while we can determine average decay rates and make probabilistic predictions for a large number of nuclei, the exact decay probability for a single nucleus at a given moment cannot be calculated.