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Carbon-14 in a dead animal

  1. Jul 2, 2012 #1
    Im having trouble answering this question.

    How long it takes for 80% of the carbon-14 to decay in an animal after it has died.
    Carbon decays rate 0.012% per year.

    So, my understanding is,

    -(R = 0.00012 yr-1, t=1 yr)
    R=Ro exp (-λt)
    0.00012=Ro exp(-λ(1)) ---- (1)

    -No = 0.8,
    No=λRo
    Ro=0.8/λ ------ (2)

    To find λ, (2) into (1)

    0.00012=0.8/λ exp(-λ(1))
    ∴ λ = 8.8 yrs-1

    Now im stuck which equation i have to use to find the year?
    Are my assumption above is correct?
     
  2. jcsd
  3. Jul 2, 2012 #2

    mfb

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    Staff: Mentor

    R=Ro exp (-λt) is the activity of the sample (decays per time)
    0.00012/yr is the relative activity (decays per atoms per year)
    They have a different meaning.

    If 0.00012 of the probe decays per year, after one year the number of radioactive atoms and the activity is 0.99988 of its original value:

    0.99988=1 exp (-λt) with t=1year. Can you use this equation to find λ?
     
  4. Jul 2, 2012 #3
    so i can just assume the Ro=100% although it is given No=80%?
     
  5. Jul 3, 2012 #4
    λ = - ln (0.99988) [in units of inverse years]

    Then solve e-λt = 0.2 for t using the above...
     
  6. Jul 3, 2012 #5

    mfb

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    Staff: Mentor

    No this is not given. It is given that 20% remains, which means R=0.2 R0 and N=0.2 N0
     
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