Question

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?

Answer 1

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

(1/2) = e^(-kh)
Where:
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.
Given:
1[mole]=6.02214129(27)E+23[atoms]
U[238] weighs 238.05078822[g/mol]

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