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.

Question

$^{10_{5}$B + $^{4}_{2}$He $\rightarrow$ X + $^{1}_{0}$n. In the above nuclear reaction, X will be}

Answer 1

To determine the age, employ the following formula:

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

With the ratio $\frac{(^{14}C/^{12}C)_{\text{sample}}}{(^{14}C/^{12}C)_{\text{initial}}} = \frac{1}{8}$,

The age is calculated as: t = $\ln 8 \times \frac{5730}{\ln 2} = 17190$ 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.