Question

The piece of wood from a recently cut tree shows $20$ decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If half life of $C^{14}$ is $5730$ years, then age of the wooden piece placed in the museum is approximately

• A. $10439$ years
• B. $13094$ years
• C. $19039$ years
• D. $39040$ years

Answer 1

Answer: (C)

$19039$ years

We know that:
$A=A_o{e}^{-\lambda t}$

Therefore,
$2=20e^{-\lambda t}$
$t=\frac{log10}{\lambda }$

Also,
$\lambda =\frac{log2}{t_{\left(1/2\right)}}$

Solving above equations, we get:
$t=19039years$