SOLUTION: An unknown radioactive element decays into non-radioactive substances. In 840 days the radioactivity of a sample decreases by 48 percent. (a) What is the half-life of the elemen

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Question 1088848: An unknown radioactive element decays into non-radioactive substances. In 840 days the radioactivity of a sample decreases by 48 percent.
(a) What is the half-life of the element?

(b) How long will it take for a sample of 100 mg to decay to 69 mg?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
The half-life formula is
:
N(t) = N(0) * (1/2)^(t/t(1/2))
:
solve for t(1/2)
:
1) t(1/2) = t / (log(1/2)(N(t)/N(0))
:
let N(0) = 1.0 and N(t) = (1.0 - 0.48) = 0.52 and t = 840
:
t(1/2) = 840 / (log(1/2) (0.52/1.0)) = 893.6 approx 894 days
:
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a) half-life is 894 days
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solve equation 1) for t
:
t = t(1/2) * (log(1/2)(N(t)/N(0))
:
t = 894 * log(1/2) (69/100) = 894 * 0.535 = 478.29 approx 478
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b) it will take 478 days for sample to decay from 100 mg to 69 mg
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