### 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