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Carbon dating

  1. Jan 6, 2014 #1
    1. The problem statement, all variables and given/known data
    Suppose you have a 1.4g sample of old charcoal. It produces 0.7 beta decays per minute. How old is the charcoal.

    Given:
    1g of carbon current day has 6.36x1010 atoms of 14C


    2. Relevant equations

    N = Noe-rt

    N = number of atoms in the sample (current-day)
    No = original number of atoms (i.e. at time of death)
    r = decay rate = 1.21x10-4
    t = time

    3. The attempt at a solution

    I know that No = 1.4*6.36x1010 = 8.904x1010
    r = 1.21x10-4

    what I don't understand is what to do with the 0.7 decays per minute. I know I need to solve for N before I can solve for t, but I'm stuck. As soon as I solve for N, it's plug and chug.

    Any help would be much appreciated!
     
  2. jcsd
  3. Jan 6, 2014 #2

    SteamKing

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    It would be helpful to know the units of the decay rate r.
     
  4. Jan 6, 2014 #3

    ehild

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    If you have N C14 atoms, how many of them decays in unit time? How is it related to the decay rate?

    ehild
     
  5. Jan 6, 2014 #4
    r = 1.21x10-4 /year


    If I have N C-14 atoms, then 0.7 of those N atoms decay each minute.. 0.7 decay/minute = 367920 atom decays per year.

    I'm not sure how it's related to the decay rate. Sorry, I haven't done a problem with two rates before and it's really confusing.
     
  6. Jan 6, 2014 #5

    ehild

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    N is the number of the 14C atoms in the sample at present. N0 was the number of atoms when the sample got isolated. N=N0e-rt, so dN/dt=-rN0e-rt=-rN.

    rN atoms decays in a year, that is about 368000 in the 1.4 g sample. You know r. What is N then?
    Originally there were 6.36x1010atoms of 14C in 1 g sample. Current-day means "fresh" sample, which can interact with the surroundings, so has supply of 14C. The charcoal is isolated, so the number of 14C atom decreases with time.

    ehild
     
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