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  • 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.

4.14   The half-life for radioactive decay of ^{14} C 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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best_answer

Given ,
half-life of radioactive decay = 5730 years
So,     t_{1/2}= 0.693/k
           k = 0.693/5730 per year

we know that, for first-order reaction,
t = \frac{2.303}{k} \log\frac{[R_{0}]}{[R]}
t = \frac{2.303}{.693/5730} \log\frac{100}{80}             
    = 1845 years (approximately)

Thus, the age of the sample is 1845 years

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manish

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