1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Shooting Star

    User Avatar
    Homework Helper


    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

    Shooting Star

    User Avatar
    Homework Helper

    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 :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Half life and the age of a planet
  1. Half life (Replies: 7)

  2. Half Life Problem (Replies: 1)

  3. Half life/Mean life (Replies: 1)