Question

Equal masses of two samples A and B of charcoal are burnt and the activity of resulting carbon dioxide from two samples is measured. The gas from sample A gives $10$${}^4$ counts per month and that from sample B gives $2.5$ x$10$${}^3$counts per month. The age difference of two samples is ( half life of $C^{14}$ is $5730$ years)

• A. $5730$ years
• B. $11460$ years
• C. $17190$ years
• D. $22920$ years

Answer 1

The correct option is B $11460$ years

Rate of gas A $={10}^{4}counts/month=\lambda N_1$

where, $N_1=N_0{e}^{-\lambda t_1}\cdot \cdot \cdot \left[1\right]$

And same for gas B:

Rate of gas B $=2.5\times {10}^{3}counts/month=\lambda N_2$

where, $N_2=N_0{e}^{-\lambda t_2}\cdot \cdot \cdot \left[2\right]$

Dividing [1] and [2] ,

$\Rightarrow \frac{100}{2.5\times {10}^3}=e^{-\lambda (t_2-t_1)}$

$\Rightarrow ln4=\frac{ln2}{5730}(t_2-t_1)$

$\Rightarrow$ Difference $=2\times 5730years$
$=11460years$