decay stages are referred to by their relationship to previous or subsequent stages. a parent isotope is one that undergoes decay to form a daughter isotope. one example of this is uranium (atomic number 92) decaying into thorium (atomic number 90). the daughter isotope may be stable or it may decay to form a daughter isotope of its own. the daughter of a daughter isotope is sometimes called a granddaughter isotope.
the time it takes for a single parent atom to decay to an atom of its daughter isotope can vary widely, not only between different parent-daughter pairs, but also randomly between identical pairings of parent and daughter isotopes. the decay of each single atom occurs spontaneously, and the decay of an initial population of identical atoms over time t, follows a decaying exponential distribution, e−λt, where λ is called a
the intermediate stages each emit the same amount of radioactivity as the original radioisotope (i.e. there is a one-to-one relationship between the numbers of decays in successive stages) but each stage releases a different quantity of energy. if and when equilibrium is achieved, each successive daughter isotope is present in direct proportion to its half-life; but since its activity is inversely proportional to its half-life, each nuclide in the decay chain finally contributes as many individual transformations as the head of the chain, though not the same energy. for example, uranium-238 is weakly radioactive, but