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29 March, 10:09

How much of a sample remains after five half-lives have occurred?

1/5 of the original sample

1/25 of the original sample

1/32 of the original sample

1/64 of the original sample

BOB

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  1. 29 March, 13:07
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    1/32 of the original sample

    Explanation:

    We have to use the formula

    N/No = (1/2) ^t/t1/2

    N = amount of radioactive sample left after n number of half lives

    No = original amount of radioactive sample present

    t = time taken for the amount of radioactive samples to reduce to N

    t1/2 = half-life of the radioactive sample

    We have been told that t = five half lives. This implies that t = 5 (t1/2)

    N/No = (1/2) ^5 (t1/2) / t1/2

    Note that the ratio of radioactive samples left after time (t) is given by N/No. Hence;

    N/No = (1/2) ^5

    N/No = 1/32

    Hence the fraction left is 1/32 of the original sample.
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