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27 October, 10:40

25. Iodine-131 is a radioactive substance that can be used to treat certain thyroid conditions. It has a

balf-life of 8 days. Your friend with a thyroid condition is given 40 mg of I-131 to drink. Assuming

that all the l-131 stays in her body, how much will remain after 4 half-lives?

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  1. 27 October, 10:58
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    2.5 mg of I-131

    Explanation: Half life refers to the time taken by a radioactive isotope to decay to a half of its initial amount. For example, if the half-life of I-131 is 8 days, it will take 8 days for a mass of 100 g of I-131 to decay to 50 g.

    In this case, we are given;

    Initial mass of I-131 is 40 mg

    Half life of I-131 is 8 days

    Number of half lives is 4.

    We are required to determine the mass that will remain after 4 half lives.

    Using the formula;

    Remaining mass after decay = Initial mass before decay * (1/2) ^n, where n is the number of half lives.

    Therefore;

    Remaining mass = 40 mg * (1/2) ^4

    = 40 mg * 1/16

    = 2.5 mg

    Hence, the mass I-131 remaining in her body after 4 half-lives will be 2.5 mg.
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