SOLUTION: The half-life of 234U, uranium-234, is 2.52 105 yr. If 98.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The half-life of 234U, uranium-234, is 2.52 105 yr. If 98.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?       Log On


   

Question 600575: The half-life of 234U, uranium-234, is 2.52 105 yr. If 98.9% 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):
You can put this solution on YOUR website!
The half-life of 234U, uranium-234, is 2.52 105 yr.
Probably mean 2.52(10^5) yrs.
If 98.9% 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 = resulting amt after t time
A0 - initial amt (t=0)
t = time of decay
h = half-life of substance
:
Let initial amt = 1
1*2^(-t/(2.52(10^5)) = .989
use common logs
-t%2F%282.52%2810%5E5%29%29*log(2) = log(.989)
-t%2F%282.52%2810%5E5%29%29 = log%28.989%29%2Flog%282%29
Find the logs
-t%2F%282.52%2810%5E5%29%29 = -.01596
t = -.01596*-2.52(10^5)
t = 4021.3 ~ 4000 yrs