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2023-03-12

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. Calculate the sample's age.

kumukep44

Here, $k=\frac{0.693}{{t}_{1/2}}$
$=\frac{0.693}{5730}year{s}^{-1}$
It is known that,
$t=\frac{2.303}{k}\mathrm{log}\frac{\left[R{\right]}_{0}}{\left[R\right]}$
$=\frac{2.303}{\frac{0.693}{5730}}log\frac{100}{80}$
= 1845 years (approximately)
Hence, the age of the sample is 1845 years.

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