The amount of isotope in an ancient piece of wood is found to be exactly one-fifth () of that presen — Chemical Kinetics Chemistry Question
Question
The amount of ${}^{14}C$ isotope in an ancient piece of wood is found to be exactly one-fifth ($1/5$) of that present in a fresh piece of wood. Assuming the half-life of ${}^{14}C$ is $5770 \text{ years}$, which of the following expressions correctly calculates the age of the wood?
Answer: A
💡 Solution & Explanation
The rate constant $k = 0.693 / 5770$. The age $t$ is calculated using $t = (2.303 / k) \log([A]_0 / [A]_t)$. Here, $[A]_0 / [A]_t = 5$ (since $[A]_t = 1/5 [A]_0$). Substituting $k$ gives $t = \frac{2.303 \times 5770}{0.693} \log 5$.
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