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Homework Help: Calculating Radioactive Decay

  1. Oct 30, 2005 #1
    The carbon in living matter contains a fixed proportion of the radioactive isotope carbon-14. The carbon-14 in 1.00g of carbon from living matter has an activity of 0.250Bq. The half-life of carbon-14 is 5730. When a plant dies the proportion of carbon-14 decreases due to radioactive decay. A 1.00g sample of carbon from an ancient boat has an activity of 0.160Bq. Determine the age of the board.

    Here's how I solved it...

    Original Activity = 0.25Bq
    Activity of Sample = 0.16Bq

    Then I just calculated what's that as a ratio of the original activity...

    0.16/0.25 = 0.64

    Then multiplied the half time by this number:

    5730 * 0.64 = 3666 years ~ 3700 years

    Which is the correct answer. However this seems like a bit of a fluke. Especially since I've got a feeling I should be using this formula:

    x = x(original) ^-(lamda)*(time)

    Can anyone put my mind at ease, was my answer a fluke or is that a valid method to calculating the answer?
  2. jcsd
  3. Oct 30, 2005 #2
    Well if you do it your way you aren't really considering the fact that it's an exponential decay.
    I would say that you would use the activity equation given by:
    [tex]A=A_oe^-^\lambda ^t[/tex]
    It's just as easy. Just rearrange it and then take the natural log of both sides to solve for t.
    Where [tex]\lambda=ln(2)/T_1_/_2[/tex]
    Last edited: Oct 30, 2005
  4. Oct 30, 2005 #3
    Thanks a lot!!
    Last edited: Oct 30, 2005
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