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The decay of an unstable atomic nucleus is a random process, and we cannot predict exactly when a particular nucleus will decay. However, we can determine the probability of decay within a given time frame using a concept known as the half-life.

The stability or instability of an atomic nucleus is determined by the balance between the forces that hold the nucleus together and the forces that tend to pull it apart. In some nuclei, this balance is not ideal, leading to an excess of either protons or neutrons or both. This imbalance creates an unstable nucleus that seeks to achieve a more stable configuration.

There are several types of nuclear decay, including alpha decay, beta decay, and gamma decay. In each case, the decay occurs when the nucleus spontaneously emits particles or energy in order to reach a more stable state. The exact mechanism underlying the decay process depends on the specific type of decay.

The timing of decay events is governed by quantum mechanics. According to quantum mechanics, the decay of a nucleus is a probabilistic event. The probability of decay is described by an exponential decay law, which relates to the half-life of the radioactive material. The half-life is the time it takes for half of the radioactive nuclei in a sample to decay.

While we cannot predict when a specific nucleus will decay, we can make statistical predictions based on the half-life and the number of unstable nuclei present. This allows us to estimate the rate of decay and make practical use of radioactive materials in various fields such as medicine, industry, and scientific research.

It's important to note that the decay of individual atomic nuclei is random, but on a large scale, the behavior of a collection of unstable nuclei follows statistical patterns, which enable us to describe and understand radioactive decay.

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