Question

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.

Answer 1

$k = \frac {0.693}{t_{\frac 12}}$

$k = \frac {0.693}{5730\ years}$

$It\ is\ known\ that,$

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

$t = \frac {2.303}{\frac {0.693}{5730} }log \frac {100}{80}$

$t = 1845\ years\ (approximately)$

$Hence,\ the\ age \ of \ the\ sample \ is \ 1845\ years.$