SOLUTION: uranium-235 is used as fuel for some nuclear reactors. it has a half life of 710 million years. how long will it take 10 grams of uranium-235 to decay to 1 gram?

Question 230272: uranium-235 is used as fuel for some nuclear reactors. it has a half life of 710 million years. how long will it take 10 grams of uranium-235 to decay to 1 gram?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
uranium-235 is used as fuel for some nuclear reactors.
it has a half life of 710 million years. how long will it take 10 grams of uranium-235 to decay to 1 gram?
;
The half life equation
Ao*2^(-t/h) = A
where
A is the resulting amt (1)
Ao is the initial amt (10)
t = time (in millions of yrs in this case)
h = half-life of the substance (in millions of yrs) (710)
:
10*2^(-t/710) = 1
:
divide both sides by 10
2^(-t/710) =
2^(-t/710) = .1
:
use logs here
log(2^(-t/710)) = log(.1)
;
log equiv of exponents
*log(2) = log(.1)
:
*.301 = -1
:
=
:
-t = 710*
t = 2,358.569 million yrs
;
:
Check this on good calc: enter 10*2^(-2358.569/710) ~ 1.0

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