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Radioactive decay of CaCO3

  1. Jun 10, 2017 #1
    1. The problem statement, all variables and given/known data
    Archeologists removed some charcoal from a Native American
    campfire, burned it in O2, and bubbled the CO2 formed into
    Ca(OH)2 solution (limewater). The CaCO3 that precipitated was
    filtered and dried. If 4.58 g of the CaCO3 had a radioactivity of
    3.2 d/min, how long ago was the campfire?

    2. Relevant equations
    C + O2 --> CO2
    CO2 + Ca(OH)2 --> CaCO3 + H2O
    3. The attempt at a solution
    Activity = kN
    So k = Activity/N = (3.2 atoms/min)/(0.04576 mol * 6.022*10^23 atoms/mol)
    = 1.2*10^-22 min^-1
    half life = ln2/k
    = 5.776*10^21 min

    And that's all I know..I don't have the initial and final moles of the CaCO3, so how should I calculate the time that passed?
  2. jcsd
  3. Jun 10, 2017 #2


    User Avatar

    Staff: Mentor

    You can easily calculate total amount of carbon, and I bet your textbook (or lecture notes) states what is the typical fraction of C-14 in natural samples. If not, you will need to look for this information.

    Note, that in reality this is not a single number, as the fraction of C-14 in the atmosphere is not constant. There are tables that can be used to find more precise data.
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