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Exponential dsn. please check my work

  1. Nov 22, 2011 #1
    A piece of rock contains 10^20 atoms of a particular substance. Each atom has an expoentially distributed lifetime with a half-life of one century. How many centurites must pass before

    there is about a 50% chance that at least one atom remains. What assumptions are you making?

    answer:

    so P (at least one survives past t) = P (no one does) = .5

    now, I'm making the assumption that Prob of survival is so small and since n is huge, this follows a poisson disn.

    thus .5 = P(k=0) = e

    then μ = ln 5

    now μ = np = 1020* e-ln 2 t. ln 2 is my parameter since half time is 1 century.

    thus t = ln(1020/ln 5) * (ln 2)-1 ≈ 65 years
     
  2. jcsd
  3. Nov 23, 2011 #2

    mathman

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    Your time unit is centuries, not years. So your answer (I didn't check arithmetic) is 65 centuries.
     
  4. Nov 23, 2011 #3
    what about the theory, is it correct?
     
  5. Nov 24, 2011 #4

    mathman

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    Above has error, μ = -ln.5 = ln2

    The general idea is correct. You might try a binomial to check. The result should be about the same.
     
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