SOLUTION: The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has      Log On


   

Question 560081: The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr.
If 97.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
:
Assume you mean the half-life uranium 234 is 2.52(10^5) yrs
:
The radioactive decay formula: A = Ao*2^(-t/h), where
A = resulting amt after t yrs
Ao = initial amt, t=0
h = half-life of substance
t = time
:
Assuming initial amt = 1
2^(-t/2.52(10^5) = .979
we will use nat logs
-t%2F%282.52%2810%5E5%29%29*ln(2) = ln(.979)
;
-t%2F%282.52%2810%5E5%29%29 = ln%28.979%29%2Fln%282%29
;
-t%2F%282.52%2810%5E5%29%29 = -.03062
:
t = %28-.03062%29%2A%28-2.52%2810%5E5%29%29
:
t = 7,716 ~ 8,000 yrs