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12 May, 05:41

The half-life of cesium-137 is 30 years. suppose we have a 200-mg sample.

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  1. 12 May, 05:53
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    a) To find the mass after t years:

    we will use this formula:

    A = Ao / 2^n

    when A = the amount remaining

    and Ao = the initial amount

    and n = t / t (1/2)

    by substitution:

    ∴ A = 200 mg / 2^ (t/30y)

    b) Mass after 90 y:

    by using the previous formula and substitute t by 90 y

    A = 200mg / 2^ (90y/30y)

    ∴ A = 25 mg

    C) Time for 1 mg remaining:

    when A = Ao / 2^ (t/t (1/2)

    so, by substitution:

    1 mg = 200 mg / 2^ (t/30y)

    ∴2^ (t/30y) = 200 mg by solving for t

    ∴ t = 229 y
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