Q. An archaeologist analysis the wood in a prehistoric structure and finds that $C^{14}$ (Half life $= 5700\ years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about
A) $5700\ years$
B) $2850\ years$
C) $11,400\ years$
D) $22,800\ years$
Explanation
(c) $\frac{C_{14}}{C_{12}} = \frac{1}{4} = \left( \frac{1}{2} \right)^{t/5700} \Rightarrow \frac{t}{5700} = 2 \Rightarrow t = 11400\ years$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.