SOLUTION: Beryllium-11 decomposes into boron-11 with a half-life of 13.8 secs. How long will it take 240g of beryllium-11 to decompose into 7.5g of beryllium-11?

Question 252184: Beryllium-11 decomposes into boron-11 with a half-life of 13.8 secs. How long will it take 240g of beryllium-11 to decompose into 7.5g of beryllium-11?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Beryllium-11 decomposes into boron-11 with a half-life of 13.8 secs. How long will it take 240g of beryllium-11 to decompose into 7.5g of beryllium-11?
.
Apply the exponential growth formula:
x(t) = xo*e^(kt)
where
x(t) is amount at time t
xo is the initial amount
k is the growth/decay rate
t is the time
.
We need to find k, do this with the info provided in the first sentence:
x(t) = xo*e^(kt)
x/2 = x*e^(k*13.8)
1/2 = e^(k*13.8)
.5 = e^(k*13.8)
ln(.5) = k*13.8
ln(.5)/13.8 = k
.
Use the above to answer the question:
x(t) = xo*e^(kt)
7.5 = 240*e^(t*ln(.5)/13.8)
7.5/240 = e^(t*ln(.5)/13.8)
ln(7.5/240) = t*ln(.5)/13.8
[ln(7.5/240)]/[ln(.5)/13.8] = t
114.84 secs = t

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