Question

What is the approximate age of the ancient tree sample if specific activity of $C-14$ in it is $\frac{1}{4}$ of the activity of newly felt trees? Half-life of $C-14$ is 5570 years.

• A. 11,140 years
• B. 5570 years
• C. 16,710 years
• D. 2785 years

Answer 1

The correct option is A 11,140 years

Decay constant
$\lambda =\frac{\ln 2}{t_{1/2}}$ = $\frac{\ln 2}{5570}$

Activity of the sample is given by
$A=\lambda N=\lambda N_0{e}^{-\lambda t}$
and activity of a fresh sample will be
$A=\lambda N_0$

Given $\frac{\lambda N}{\lambda N_0}=\frac{1}{4}$
$\Rightarrow e^{-\lambda t}=\frac{1}{4}$
$\Rightarrow \ln \left(1/4\right)=-\lambda t$
$\Rightarrow t=\frac{2\ln 2}{\lambda }$
This gives
$t=2\times 5570=11,140$ years