Question:
The ratio of \(\frac{{^{14}\text{C}}}{{^{12}\text{C}}}\) in a piece of wood is \(\frac{1}{8}\) part that of atmosphere. If the half-life of \(^{14}\text{C}\) is 5730 years, the age of the wood sample is _______ years.
The ratio of \(\frac{{^{14}\text{C}}}{{^{12}\text{C}}}\) in a piece of wood is \(\frac{1}{8}\) part that of atmosphere. If the half-life of \(^{14}\text{C}\) is 5730 years, the age of the wood sample is _______ years.
Updated On: Nov 15, 2024
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Correct Answer: 17190
Solution and Explanation
The age can be calculated using:
t = \(\left(\ln \frac{(^{14}C/^{12}C)_{\text{initial}}}{(^{14}C/^{12}C)_{\text{sample}}}\right) \frac{t_{1/2}}{\ln 2}\)
Given \(\frac{(^{14}C/^{12}C)_{\text{sample}}}{(^{14}C/^{12}C)_{\text{initial}}} = \frac{1}{8}\),
t = \(\ln 8 \times \frac{5730}{\ln 2} = 17190\) years
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