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The half life of U238 is 4.5 x 10^9 yr. A sample of rock of 1.6 g produces 29 dis/sec. Assuming all radioactivity is due to U238 find percent by mass of U 238.

I have tried
ln(t)/ln(0)= -kt and still cannot get the answer
What I get is
A) 4.5x10^9 x365x60x60x24=1.419x10^17 for half life
B) .693/1.419x10^17=4.883x10-18

C) ln t/ln 29= -(4.883x10^-18)

That is the farthest I've gotten. Can someone help?

  • Chemistry -

    Use Nt/N0 = e^{-kt}
    1[yr] = a = 31557600[s]

    (1/2) = e^(-kh)
    Half life: h= 4.5e9 * a = 1.420092E+17[s]

    k = -ln(0.5)/1.420092E+17
    .: k = 4.8810019E-18[/s]

    Okay, so far. To continue...
    Assume there is n atoms of U238 in the sample. t=1 second latter there is n-29. (via 29 disintegrations per second)

    (n-29)/n = e^{-kt}
    1 - (29/n) = e^{-kt}
    29/n = 1-e^{-kt}
    n = 29/(1-e^{-kt})
    n = 29/(1-exp(-4.8810019E-18))
    n = 5.9414031E+18[atoms]

    Next: find the weight of this number.
    U[238] weighs 238.05078822[g/mol]

    Express as a percentage of the sample weight (1.6[g]).

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