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The half-life of cobalt 60 is 5.25 yrs. ...

The half-life of cobalt `60` is `5.25` yrs. After how long does its acitvity reduce to about one eight of its original value?

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The activity is proportional to the number of undecayed atoms. In each half-life, the remaining sample decays to half of its initial value. Since `(1/2)xx (1/2) xx (1/2) = 1/8` therefore three half-lives or `15.75` years are required for the sample to decay to `1//8th` its original strenth.
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