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14 November, 13:41

Americium-241 is used in some smoke detectors. it is an alpha emitter with a half-life of 432 years. how long will it take in years for 45.0 % of an am-241 sample to decay?

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  1. 14 November, 15:26
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    The amount of substance at a certain time t, At, with half-life of h is determined by the equation,

    At = (Ao) (0.5) ^ (t/h)

    where Ao is the original amount.

    From the given,

    At/Ao = 0.45 = (0.5) ^ (t/432)

    The value of t from the equation is 497.67 years.
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