Chemistry
posted by Nancy on .
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=4.883x1018
C) ln t/ln 29= (4.883x10^18)
That is the farthest I've gotten. Can someone help?

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 = 4.8810019E18[/s]
Okay, so far. To continue...
Assume there is n atoms of U238 in the sample. t=1 second latter there is n29. (via 29 disintegrations per second)
(n29)/n = e^{kt}
1  (29/n) = e^{kt}
29/n = 1e^{kt}
n = 29/(1e^{kt})
n = 29/(1exp(4.8810019E18))
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]).