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Homework Help: Decay Constant

  1. May 5, 2004 #1
    Carbon14 has a half life of 5730 yrs. This is the only information i am given.

    Caluculate the decay constant of Carbon 14.

    This is what I have done.

    dN/dt = -lambda(N)

    I know the Avogadro Constant is equal to 6x10^23

    So i am using 1kg in my formula.

    14C = 6 x 10^23 x 1000/14

    where do i go from here??
  2. jcsd
  3. May 5, 2004 #2

    Doc Al

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    Staff: Mentor

    Half life and decay constant are just two ways of expressing the rate of radioactive decay. Half life (T) uses a base of 2:
    [tex]X = X_0 2^{-\frac{t}{T_{half}}}[/tex]

    Decay constant (λ) uses a base of "e":
    [tex]X = X_0 e^{-\lambda t}[/tex]

    You can convert from one to the other. Hint: [tex]2 = e^?[/tex]
  4. May 5, 2004 #3
    ok i used dN/dt

    which is 0.693 x 6 x 10^23/5730x 360 x 24 x 3600 x 14
    which is equal to 3 x 10^28 s^-1

    Is that right??
  5. May 5, 2004 #4


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    Science Advisor
    Gold Member

    Remeber that 1/λ is going to be equal to the mean lifetime of a C-14 particle, your figure gives a mean lifetime of about 3 x 10^-29 seconds, the mean lifetime is always longer than the half-life so the anbswer MUST be wrong.

    Use Dr. Al's hints.
  6. May 5, 2004 #5

    Doc Al

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    Avogadro's number is irrelevant.
    [tex]2 = e^{0.693}[/tex]
    so... [itex]\lambda = \frac{0.693}{T_{half}}[/itex]
  7. May 5, 2004 #6
    Ah i dont understand it.
    Im looking at an example in a book and it has the second formula he gives,

    ie N=No e^-lambda t

    therefore dN/dt=-No Lambda e ^-lambda t = - lambda N

    When N =12, dN/dt = -lambda 10^12

    Now lambda = 0.693 / T1/2
  8. May 5, 2004 #7

    Doc Al

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    Staff: Mentor

    decay rate vs. decay constant?

    Perhaps you are confusing decay rate (which is dN/dt) with decay constant (which is λ)?
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