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Question

Chemistry Question on Nuclear Chemistry

The ratio of 14C12C\frac{{^{14}\text{C}}}{{^{12}\text{C}}} in a piece of wood is 18\frac{1}{8} part that of atmosphere. If the half-life of 14C^{14}\text{C} is 5730 years, the age of the wood sample is _______ years.

Answer

The age can be calculated using:

t = (ln(14C/12C)initial(14C/12C)sample)t1/2ln2\left(\ln \frac{(^{14}C/^{12}C)_{\text{initial}}}{(^{14}C/^{12}C)_{\text{sample}}}\right) \frac{t_{1/2}}{\ln 2}

Given (14C/12C)sample(14C/12C)initial=18\frac{(^{14}C/^{12}C)_{\text{sample}}}{(^{14}C/^{12}C)_{\text{initial}}} = \frac{1}{8},

t = ln8×5730ln2=17190\ln 8 \times \frac{5730}{\ln 2} = 17190 years