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March 27, 2017

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A sample of a radioactive substance decayed to 93.5% of its original amount after a year.

a) What is the half-life of the substance?
? years

(b) How long would it take the sample to decay to 10% of its original amount?
? years

  • Calc - ,

    a) Let the half life in years be H
    2^-(1/H) = 0.935
    Solve that for H.
    -1/H log 2 = log 0.935
    -1/H = -0.09696
    H = 10.31 years

    b) Solve 2^-(t/10.31) = 0.10
    t will be the time required to decasy to 10% activity

    You could also solve
    (0.935)^t = 0.1
    The answer should be the same either way you do it: about 30 years.

  • Calc - ,

    Thank you!

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