Question

A fossilised bone is found to contain $0.1\%$ of its original C14. Find the age of the fossil.

• A. $57100$ years
• B. $43100$ years
• C. $27860$ years
• D. None of these

Answer 1

The correct option is A $57100$ years

Given that after some time period the fossilised bone is found to contain only $0.001th$ of the intial amount,

We know the decay algorithm,

i.e.,$-\frac{dx}{dt}=\frac{0.693}{\lambda }\left(x\right)$ Where $\lambda$ is the half life time period.

Solving that gives, $x=x_0{e}^{-kt}$ where, $k=\frac{0.693}{\lambda }$ and $x_0$ is the initial amount taken.

We know that half life time period for $C14$ is $5730$ years

$0.001=e^{-\frac{0.693}{5730}t}$

Solving that, gives $t=57100$ years (approx)