Question

The $C^{14}$ to $C^{12}$ ratio in a certain piece of wood is $25$% of that in atmosphere. The half life period of $C^{14}$ is $5,580$ years. The age of wood piece is

• A. $5,580$ years
• B. $2790$ years
• C. $1395$ years
• D. $11,160$ years

Answer 1

The correct option is D $11,160$ years

Let the $C^{14}:C^{11}$ ratio in atmosphere be $x$, and that in the wood be $x/4$.

Thus we get the formula for the age of wood as:

$t=\frac{t_{1/2}}{0.693}ln\left[\frac{C^{14}:C^{11}ratioinatmosphere}{C^{14}:C^{11}ratioinwood}\right]$

$t=\frac{5580\times ln4}{0.693}=11160years$