SOLUTION: Plutonium 239 is used as fuel for some nuclear reactors, and also as the fissionable material in atomic bombs. it has a half life of 24400 years. how long would it take 10 grams o

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Plutonium 239 is used as fuel for some nuclear reactors, and also as the fissionable material in atomic bombs. it has a half life of 24400 years. how long would it take 10 grams o      Log On


   

Question 379009: Plutonium 239 is used as fuel for some nuclear reactors, and also as the fissionable material in atomic bombs. it has a half life of 24400 years. how long would it take 10 grams of plutonium 239 to decay to 1 gram?(round your answer to three significant digits)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Plutonium 239 is used as fuel for some nuclear reactors, and also as the
fissionable material in atomic bombs.
it has a half life of 24400 years. how long would it take 10 grams of
plutonium 239 to decay to 1 gram?(round your answer to three significant digits)
:
The half life formula: Ao*2^(-t/h) = A
where
A = resulting amt after t yrs
Ao = initial amt
t = time in yrs
h = half-life of substance
:
10*2(-t/24400) = 1
Divide both sides by 10
2(-t/24400) = .1
Using nat logs
ln(2(-t/24400)) = ln(.1)
-t%2F24400ln(2) = ln(.1)
-t%2F24400 = ln%28.1%29%2Fln%282%29
Using a calc
-t%2F24400 = -3.32193
Multiply both sides by -24400
t = 81,055.0456 years
:
:
Check solution on a calc; enter 10*2^(-81055/24400) results: 1.000