Question

The amount of ${}_6^{14}C$ isotope in a piece of wood is found to be one-fifth of that present in a fresh piece of wood. Calculate the age of wood. (Half life of ${}^{14}C=5577$ years)

Answer 1

We know that, $t=\frac{2.303\times t_{1/2}}{0.693}\log \left(\frac{N_0}{N}\right)$
Given, $N=\frac{N_0}{5}$
So, $t=\frac{2.303\times 5577}{0.693}\log 5$
or $t=\frac{2.303\times 5577}{0.693}\times 0.6989=12953$ years