Question

The $C^{14}$ to $C^{12}$ ratio in a wooden article is 13% that of the fresh wood. Calculate the age of the wooden article. Given that the half-life of $C^{14}$ is 5770 years

• A. 16989 years
• B. 16858 years
• C. 15675 years
• D. 17700 years

Answer 1

Answer: (A)

16989 years

Answer 2

$\frac{N}{N_{o}} = \left( \frac{1}{2} \right)^{\frac{T}{t_{1/2}}} \Rightarrow \frac{13}{100} = \left( \frac{1}{2} \right)^{\frac{T}{5770}}$

Taking log $\Rightarrow \log\frac{13}{100} = \frac{T}{5770}\log 1/2 \Rightarrow 16989yrs$