Question

When characoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegratons of ${}^{14}$C per gram per minute. A sample from an ancient piece of charcoal shows ${}^{13}$C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of ${}^{13}$C is 5730 y.

Answer 1

Given $A_0$ = 15.3, A = 12.3,

$t_{\frac{1}{2}}$ = 5730 years

$\lambda =\frac{0.6931}{t_{\frac{1}{2}}}=\frac{0.6931}{5730}y{r}^{-1}$

Let the time passed be t,

We know A = $A_{0}e\frac{0.6931}{5730}\times t$

$\Rightarrow$ In $\frac{12.3}{15.3}=\frac{-0.6931}{5730}t$

$\Rightarrow 0.218253=\frac{0.6931}{5730}\times t$

$\Rightarrow t$ = 1804.3 years