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Question: An archaeologist analyses the wood in a prehistoric structure and finds that \(C^{14}\) (Half life =...

An archaeologist analyses the wood in a prehistoric structure and finds that C14C^{14} (Half life = 5700 years) to C12C^{12}is only one- fourth of that found in the cells buried plants. The age of the wood is about.

A

5700 years

B

2850 years

C

11,400 years

D

22,800 years

Answer

11,400 years

Explanation

Solution

C14C12=14=(12)t/5700t5700=2t=114006muyears\frac{C_{14}}{C_{12}} = \frac{1}{4} = \left( \frac{1}{2} \right)^{t/5700} \Rightarrow \frac{t}{5700} = 2 \Rightarrow t = 11400\mspace{6mu} years