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