Question

The activity of a sample of wood is due to the presence of $50\%$ of ${}^{14}C$ as compared to the original sample. If has life of ${}^{14}C$ is $5760years$, the life of the sample of wood is:

• A. $5760years$
• B. $5670years$
• C. $6667years$
• D. $5000years$

Answer 1

The correct option is A $5760years$

$t_{1/2}=\frac{0.693}{k}$

therefore; $K=\frac{0.693}{5760}{y}^{-}1$

Now, $t=\frac{2.303}{K}lo{g}_{10}\frac{Na}{N}$

$=\frac{2.303}{K}\ast lo{g}_{10}^2$

$=\frac{L{n}^2}{K}$

$=L{n}^{2}0.693\ast 5760$ years

$T=5760$ years.