Half-Life and the Decay Law

Although the decay of any single radioactive nucleus is completely unpredictable, the behavior of a large number of nuclei together is highly regular. This is because radioactive decay is a statistical process: with billions of nuclei present, the fraction that decays in a given time is very consistent. The key idea is that in any given interval, a fixed proportion of the remaining nuclei will decay. This leads to a smooth, predictable decrease in the number of undecayed nuclei over time, described by the exponential decay law.

The activity of a source, denoted $A$ (not to be confused with mass number), is the number of nuclear decays occurring per second. Its SI unit is the becquerel (Bq), where one becquerel equals one decay per second. The activity is proportional to the number of undec