Chemical Kinetics Question 1
Question 1 - 2024 (01 Feb Shift 1)
The ratio of $\frac{{ }^{14} \mathrm{C}}{{ }^{12} \mathrm{C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of ${ }^{14} \mathrm{C}$ is 5730 years, the age of wood sample is _______ years.
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Answer (17190)
Solution
$\lambda t=\ln \frac{\left({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\right){\text {atmosphere }}}{\left({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\right){\text {wood sample }}}$
As per the question,
$\frac{\left({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\right){\text {wood }}}{\left({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\right){\text {atmosphere }}}=\frac{1}{8}$
So, $\lambda t=\ln 8$
$\frac{\ln 2}{t_{1 / 2}} \mathrm{t}=\ln 8$
$\mathrm{t}=3 \times \mathrm{t}_{1 / 2}=17190$ years
