The Bateman equation refers to a set of equations used in nuclear physics and radiochemistry to describe the behavior of radioactive decay chains. Specifically, it models the quantity of a radioactive isotope over time, taking into account both its decay and the potential decay of its progeny in a decay chain. For a single radioactive isotope, the Bateman equation can typically be expressed mathematically to relate the amount of a parent nuclide to its time-dependent quantities.
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The Bateman equation gives the populations in a sequential radioactive decay chain. For a parent with population and an initially absent daughter, distinct decay constants give ; the first population satisfies .