## Quick Reference

The equilibrium reached by a radioactive series in which the rate of decay of each nuclide is equal to its rate of production. It follows that all the rates of decay of the different nuclides within the sample are equal when radioactive equilibrium is achieved. For example, in the **uranium series**, uranium–238 decays to thorium–234. Initially the rate of production of thorium will exceed the rate at which it is decaying, and the thorium content of the sample will rise. As the amount of thorium increases, its activity increases; eventually a situation is reached in which the rate of production of thorium is equal to its rate of decay. The proportion of thorium in the sample will then remain constant. Thorium decays to produce protactinium–234; some time after the stabilization of the thorium content the protactinium content will also stabilize. When the whole radioactive series attains stabilization, the sample is said to be in radioactive equilibrium. There is a simple relationship between the numbers of nuclides of a specific type and their associated half-lives: *N*_{1}/T_{1} = *N*_{2}/T_{2} = *N*_{3}/T_{3} = …, where *N*_{1}, *N*_{2}, … are the numbers of nuclides of type 1, 2, etc. *T*_{1}, *T*_{2}, … are their respective half-lives.

*Subjects:*
Physics.

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