SOLUTION: The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.7% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has

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Question 577777: The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.7% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
Please make this simple. 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 multiplied by 105 yr.
If 97.7% 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
Ao = initial amt (t=0)
h = half-life of substance
t = time in yrs
:
I think you mean the half-life of uranium-234 is: 2.52(10^5) yrs
Let Ao = 1,
A = .977
find t
:
1*2^[-t/2.52(10^5)] = .977
using logs
log%282%5E%28-t%2F2.52%2810%5E5%29%29%29+=+Log%28.977%29
log equiv of exponents
-t%2F%282.52%2810%5E5%29%29*log(2) = log(.977)
:
-t%2F%282.52%2810%5E5%29%29 = log%28.977%29%2Flog%282%29
using a calc
-t%2F%282.52%2810%5E5%29%29 = -.033569
t = -.033569%2A-2.52%2810%5E5%29
:
t = +8459.5 ~ 8000 yrs to the nearest thousand