Question

The ${}_6{C}^{14}$ and ${}_6{C}^{12}$ ratio in a piece of wood is 1/16th part to that of the atmosphere.The age of wood in years will be:
$t_{1/2}$ of $C^{14}$ 5577 years.

Answer 1

$\frac{N_{C^{14}}}{N_{C^{12}}}=\frac{1}{16}\frac{N_{0_{C^{14}}}}{N_{0_{C^{12}}}}$
Since only $C^{14}$ undergoes decay.
$\therefore \frac{N_{0_{C^{14}}}}{N_{0_{C^{12}}}}=\frac{16}{1}$
$t=\frac{2.303}{K}log\frac{16}{1}$
$=\frac{2.303}{0.693}\times 5577log{2}^4$
$=5577\times 4=22308$ years