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Nuclear decay and half-life

  1. Nov 5, 2009 #1
    1. The problem statement, all variables and given/known data
    Background info: The first order rate of nuclear decay of an isotope depends only upon the isotope, not its chemical form or temperature. The half-life for decay of carbon-14 is 5730 years. Assume that the amount of C-14 present in the atmosphere as CO2 and therefore in a living organism has been constant for the last 50,000 years. An ancient sample containing C-14 will show fewer disintegrations of the C-14 that is present than a modern sample because the concentration of C-14 is lower in the ancient sample.

    If a 1.00 gram sample of wood found in an archaelogical site in Arizona underwent 7.90x103
    disintegrations in a given time period (e.g., 20 h) and a modern sample underwent 1.84x104 disintegrations in the same time period, how old is the ancient sample?

    2. Relevant equations

    First order:
    ln[A]t = -kt + ln[A]o
    [A]t = e-kt[A]o

    ln(([A]o/2)/[A]o) = -kt1/2 = ln(1/2)
    or ln2 = kt1/2 = 0.693

    3. The attempt at a solution
    kt1/2 = 0.693
    k = 0.693/5730 = 1.21x10-4

    ln[A]t = -kt + ln[A]o
    ln[A]t = ?
    ln[A]o = ?
    Solve for t?
    Is this the right equation to use?
     
    Last edited: Nov 6, 2009
  2. jcsd
  3. Nov 6, 2009 #2

    Borek

    User Avatar

    Staff: Mentor

    t1/2 is given, simple mistake here.

    Other than that go for

    [tex]\frac {A_t} {A_0} = e^{-kt} [/tex]

    and it becomes almost simple plug and chug.

    --
     
  4. Nov 6, 2009 #3
    What do I use for At and A0?
    The number of disintegrations?
     
  5. Nov 6, 2009 #4

    Borek

    User Avatar

    Staff: Mentor

    Yes. You are interested in ratio of activities.

    --
    methods
     
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