Question

Equal masses of two samples of charcoal A and B are burnt separately and the resulting carbon dioxide are collected in two vessels. The radioactivity of ${}^{14}C$ is measured for both the gas samples. The gas from the charcoal A gives 2100 counts per week and the gas from the charcoal B gives 1400 counts per week. Find the age difference between the two samples. Half-life of ${}^{14}C$ = 5730 y.

• A. 2500 Years
• B. 3352 Years
• C. 4567 Years
• D. 2392 Years

Answer 1

The correct option is B 3352 Years

Let's start with the activity formula
$A=A_{\circ }e-\lambda t$
Now as we discussed in the hint, we need to calculate after how much time the activity reduces from 2100 counts per weak to 1400 counts per weak.
So, if we take $A_{\circ }=2100$ counts per week.
And A = 1400 counts per week
We get
$1400wee{k}^{-1}=2100wee{k}^{-1}{e}^{-\lambda t}$
We get,
$e^{-\lambda t}=\frac{2}{3}$
$t=\frac{ln\frac{3}{2}}{\lambda }$
$=\frac{ln\frac{3}{2}}{0.693}{t}_{\frac{1}{2}}$
$=\frac{0.4055}{0.693}\times 5730Years$
$=3352Years$