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18 January, 21:19

A radioactive sample has a count rate of 800 counts per minute. One hour later, the count rate has fallen to 100 counts per minute. What is the half-life of the sample?

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  1. 19 January, 00:26
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    Radioactivity equation states:

    N = No e^ (-0.693t/t1/2) - - - Where t = time, t1/2 = half-life, N = count after time t, No = Initial count

    Using the values given;

    100 = 800 e^ (-0.693*1/t1/2)

    100/800 = e^ (-0.693t/t1/2)

    0.125 = e^ (-0.693/t1/2)

    Taking natural logs on both sides;

    log 0.125 = - 0.693/t1/2 * log (e)

    -0.9031 = - 0.693/t1/2 * 0.4323

    t1/2 = (-0.693*0.4323) / (-0.9031) = 0.3317 hours

    Therefore, half-life of the sample is approximately 0.3317 hours
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