The law of radioactive decay describes the process by which unstable atomic nuclei lose energy by emitting radiation, resulting in a decrease in the number of radioactive atoms over time. This process follows an exponential decay model, meaning that the rate of decay is proportional to the amount of the substance present at any given time, leading to a predictable half-life for different isotopes. Understanding this law was crucial in the development of nuclear physics and has significant implications in various fields, including medicine and archaeology.