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?
:
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/(2.52(10^5))}}}*ln(2) = ln(.979)
;
{{{-t/(2.52(10^5))}}} = {{{ln(.979)/ln(2)}}}
;
{{{-t/(2.52(10^5))}}} = -.03062
:
t = {{{(-.03062)*(-2.52(10^5))}}}
:
t = 7,716 ~ 8,000 yrs