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The half-life for radioactive decay of 14^C is 5730 years. An archaeological artifact containing wood had only 80% of the 14^C found in a living tree. Estimate the age of the sample.

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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.

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k = \(\frac{0.693}{t_{1/2}}\)

Here,

= \(\frac{0.693}{5730}\)years-1

It is know that

t = \(\frac{2.303}{k}\)log \(\frac{[R]_0}{[R]}\)

= \(\frac{2.303}{\frac{0.693}{5730}}\)log \(\frac{100}{80}\)

= 1845 years (approximately)

Hence, the age of the sample is 1845 years.

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