A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)e^kt, where m(0) is the initial mass and k is a negative cons

A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)e^kt, where m(0) is the initial mass and k is a negative constant. The mean life M of an atom in the substance is
[infinity]
M = âk â« te^kt dt.
0

For the radioactive carbon isotope, 14C, used in radiocarbon dating, the value of k is -0.000121. Find the mean life of a 14C atom.

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  1. Answer:

    mean life = 8264.5 s

    Step-by-step explanation:

    k = – 0.000121

    The relation is given by

    [tex]m = mo e^{kt}[/tex]

    Now, the mean life is the life time for which the sample retains.

    The mean life is the reciprocal of the decay constant.  

    The relation between the mean life and the decay constant is

    [tex]\tau =\frac{1}{k}\\\\\tau = \frac{1}{0.000121} = 8264.5 seconds[/tex]

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