Answer to Question #174074 in Physics for Sam

Question

2. A wooden axe found in an Egyptian tomb is found to have an activity of 0.38Bq. This activity of an identical mass of wood cut from a living tree is 0.65Bq. Calculate the age of the wood used to make the axe.( First find the half- life of carbon -12). 

Answer 1

Activity is the number of decays within a second. Find the decay constant:

$$\lambda=\frac{\ln2}{5730}=1.21·10^{-4}\text{ yr}^{-1}.$$

Then, the activity A after a certain time t can be expressed in terms of initial activity A₀:

$$A=A_0e^{-\lambda t},\\\space\\ \frac{A}{A_0}=e^{-\lambda t},\\\space\\ t=-\frac{\ln(\frac{A}{A_0})}{\lambda}=4436\text{ yr}.$$