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Suppose 32000 radioactive nuclei are in a sample. About how many remain after two days if the half-life is 22 hrs? What is the initial activity of the sample in decays per minute?

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    Two days is 48 hours or 2.18 half-lives. The original number of radioactive nuclei, 2 days earlier, is higher by a factor 2^2.18 = 4.53, so there were N0 = 145,000 radioactive nuclei then.

    There is a formula that relates activity per molecule (k) to half life (T). It is k = ln2/T = 0.693/T

    T = 22 hours = 1320 min

    The initial activity is

    A = N0*k = (145,000)(0.693)/1320
    = 76 decays/min

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