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Question
The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample.
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Solution
Radioactive decay follows first-order kinetics.
∴ Decay constant (λ) = `0.693/t_(1//2)`
= `0.693/5730` year−1
[R]0 = 100 ...[Given]
∴ [R] = 80
t = `2.303/λ log [R]_0/[R]`
= `2.303/((0.693/5730)) log 100/80`
= `(2.303 xx 5730)/0.693 xx 0.0969` year
= 1845 years
Hence, the age of the sample is 1845 years.
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