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10 May, 20:49

This exercise uses the radioactive decay model. after 3 days a sample of radon-222 has decayed to 58% of its original amount. (a) what is the half-life of radon-222? (round your answer to two decimal places.) days (b) how long will it take the sample to decay to 15% of its original amount? (round your answer to two decimal places.)

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  1. 10 May, 21:45
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    a) T = 3.82 days b) t=1.05 days

    Explanation:

    (a)

    The radioactive decay model is given by the mathematical expression that defines the exponential decrease, which can be expressed as:

    N = N0 · 0.5 t/T

    Beaing

    T = half life in days

    t = days

    N0 = Number of atoms initially

    N = Number of remaining atoms

    N (t) = N0 (0.5) t/T

    For the data of the problem, it is necessary to know:

    N (t) / N0 = %N/100

    So

    0.58 = (0.5) 3/T

    I apply logarithm to clear T

    log (0.58) = (3/T) log (0.5)

    T = 3 log (0.5) / log (0.58) days = 3.82 days

    (b)

    I use the previous formulas. So I have left

    0.15 = (0.5) t/T = (0.5) t/3.82

    log (0.15) = (t/3.82) log (0.5)

    t=3.82log (0.15) / log (0.15)

    t=1.05 days
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