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Homework Help: Finding the age of a rock

  1. Jul 19, 2008 #1
    1. The problem statement, all variables and given/known data
    The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope 40K has a 1.28 billion year half-life and is naturally present at very low levels. 40K decays by beta emission into 40Ar. Argon is a gas, and there is no argon in flowing lava because the gas escapes. Once the lava solidifies, any argon produced in the decay of 40K is trapped inside and cannot escape. A geologist brings you a piece of solidified lava in which you find the 40Ar/40K ratio to be 0.12. What is the age of the rock?

    2. Relevant equations

    where N is the number of nuclei, N0 is the initial number of nuclei, t is time allowed to decay and t[1/2] is the half life.

    3. The attempt at a solution

    I actually do not know where to start with this one. I'm not sure how to apply the ratio given, and what variable I am even looking for, or if i'm even supposed to look at the relevant equation.

    Could someone please point me in the right direction?

    Thanks in advanced!
  2. jcsd
  3. Jul 19, 2008 #2
    Your equation can be rewritten as


    Can you see a link between the ratio N/N0 and the Ar/K ratio given in the question?
  4. Jul 19, 2008 #3
    yes I think I see the connection..

    0.12 = (1/2)t/1.28billion??

    solving for t? I don't get the right answer though

    ln(.12) = t/1.25billion(ln.5) is what I was trying..
  5. Jul 19, 2008 #4
    You'll need to be careful about the value you use for the N/N0 ratio. N is the number of undecayed parent nuclei, not the daughter nuclei formed from the radioactive decay.
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