Half-life

The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay. The term also has pharmaceutical and other uses.

Decay by two or more processes

A radioactive element may decay via two or more different processes. These processes may have different probabilities of occurring, and thus there is also a different half-life associated with each process.

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As an example, for two decay modes, the amount of substance left after time t is given by

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:N(t) = N_0 e^{-lambda _1 t} e^{-lambda _2 t} = N_0 e^{-(lambda _1 + lambda _2) t}

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In a fashion similar to the previous section, we can calculate the new total half-life T _{1/2} , and we'll find it to be

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:T_{1/2} = rac{ln 2}{lambda _1 + lambda _2} ,

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or, in terms of the two half-lives

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:T_{1/2} = rac{t _1 t _2}{t _1 + t_2} ,

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Where t _1 , is the half-life of the first process, and t _2 , is the half life of the second process.

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