# The half life of carbon is 5730years.Approximately how many years will it take for 94% of a sample to decay?

$\begin{array}{1 1}(a)\;20102years&(b)\;22694years\\(c)\;23257.46years&(d)\;21262.5years\end{array}$

Carbon decay will follow first order kinetics.
So $t_{1/2}=\large\frac{ln\;2}{K}$
$K=\large\frac{ln \;2}{5730years}$
$K\times t=ln\large\frac{a}{a-x}$
$K\times t=ln\large\frac{1}{1-x/a}$
Here $x/a=0.94$
$\large\frac{ln\;2}{5730}$$t=ln\large\frac{1}{1-0.94} \large\frac{ln\;2}{5730}$$t=ln\large\frac{1}{0.06}$
$t=23257.46years$
Hence (c) is the correct answer.