SOLUTION: The half-life of 234U, uranium-234, is 2.52 105 yr. If 97.6% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? I

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Question 676393: The half-life of 234U, uranium-234, is 2.52 105 yr. If 97.6% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? I got the 97.9 = 8000 but having trouble working thru this one. thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The half-life of 234U, uranium-234, is 2.52(10^5) yr.
If 97.6% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
:
The radioactive decay formula: A =Ao*2(-t/h), where:
A = Amt after t time
Ao = initial amt (t=0)
h = half-life of substance
t = time of decay
:
Assume the initial amt is 1
1*2^(-t/(2.52(10^5)) = .976
using nat logs
-t%2F2.52%2810%5E5%29*ln(2) = ln(.976)
:
-t%2F2.52%2810%5E5%29= ln%28.976%29%2Fln%282%29
:
-t%2F2.52%2810%5E5%29= -.035047
t = -2.52(10^5) * -.035047
t = 8832 ~ 9,000 yrs