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Rates of Reaction Problem - Verification

  1. Aug 25, 2008 #1
    Hello everyone:

    For the following problem, I arrived at the correct answer but am unsure about the method used. Could someone please check my work to see if it is legitimate or if it is a fluke?

    Thank you.


    1. The age of wine can be determined by measuring the trace amount of radioactive tritium, 3H, present in a sample. Tritium gradually diminishes by a first-order radioactive decay with a half-life of 12.5 years. If a bottle of wine is found to have a tritium concentration that is 0.100 that of freshly bottled wine, what is the age of the wine?


    My Work:

    Since it takes 12.5 years for the original sample to reach 50%, I would need to find the number of half-lives needed to reach 10%.

    [tex] 0.5^x = 0.1[/tex]

    [tex] x ln 0.5 = ln 0.1 [/tex]

    [tex] x = \frac{ln 0.1}{ln 0.5} [/tex]

    Originally, I raised 12.5 to the power of
    [tex] \frac{ln 0.1}{ln 0.5} [/tex], but this was incorrect since 4404 years would be unreasonable.

    So instead:

    [tex] 12.5 x \frac{ln 0.1}{ln 0.5} = 41.5 [/tex] years, which is the right answer.

    Also, if I am indeed right, could someone please explain why I would multiply by the the number of half-lives?
    Last edited: Aug 25, 2008
  2. jcsd
  3. Aug 25, 2008 #2


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    x represents the number of half lives elapsed. So, if three half lives have elapsed, 1/8 of the original sample will remain, and (1/2)3 = 1/8. Three half lives corresponds to 12.5 x 3 = 37.5 years, not 12.53 years as the latter calculation makes no sense.
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