Question

A piece of wood was found to have ${}^{14}C/{}^{12}C$ ratio $0.6$ times that in a living plant. Calculate the period when the plant died. (Half life of ${}^{14}C=5760$ years)

Answer 1

We know that, $t=\frac{2.303\times t_{1/2}}{0.693}\log \left(\frac{N_0}{N}\right)$
So, $t=\frac{2.303\times 5760}{0.693}\log \left(\frac{1}{0.6}\right)$
$=\frac{2.303\times 5760}{0.693}\times 0.2201$
$=4213$ years