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Half life and the age of a planet

  1. Jan 29, 2008 #1
    1. The problem statement, all variables and given/known data
    An extra solar planet is discovered that is 500 light-years away. It is found through spectroscopic analysis that the abundance of potassium - 40 to potassium - 39 on the planet is 99.9%. Assuming that the planet was created with equal amounts of the two potassium isotopes, how old is the planet?

    2. The attempt at a solution
    K-39 is stable with 20 neutrons

    K-40 half life is 1.277 x 10^7 years

    K-40 decays to Ar-40 but that is stable.
    Since K-39 and K-40 were in equal proportion to begin with
    [itex]A_{0} = 0.5[/itex]
    [itex]A(t) = 0.01[/itex]

    we can use the half life equation
    [tex] A(t) = A_{0} \left(\frac{1}{2}\right)^{t/h}[/tex]
    And solving for t=8.48 x 10^7 s [/tex]

    But the light from this planet took some time to reach us - 500 light years. But that doesnt make much of a difference

    So the answer is 8.48 x 10^7 years or 6.6 half lives.

    Am i right? Please advise
  2. jcsd
  3. Jan 30, 2008 #2

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    What does the ratio mean in terms of percentage? Please check your data. Do you mean that K40 is 99.9% of the total K?
  4. Jan 30, 2008 #3
    A(t) = .999 not 0.001

    because the ratio is K-40/K-39 so there is 999 K-40 for every 1000 K-39

    is that correct??
  5. Jan 30, 2008 #4

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    That sounds a bit reasonable. Then you have to find t from:

    0.999 = 1*(1/2)^(t/h).
  6. Jan 30, 2008 #5
    Thanks for the help

    This question is solved :)
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