Question

Use Table 1: Analysis of Decay in the laboratory guide to answer this question: Scientists find a piece of wood that is thought to be from an ancient fire circle. They find that the wood contains an amount of carbon-14 (14C) that is approximately 1/16 of the current atmospheric 14C levels. Determine approximately how many years ago the tree was chopped down to be used for the firewood. If you started with 1 million carbon-14 atoms, how many atoms would remain in the wood? 14C has a t1/2 of 5,750 years.

Answer 1

We are given the initial amount of 1 million carbon-14 atoms and the final amount which is 1/16 of the current atmospheric 14C levels. Also, the half life of carbon is 5,750 years. WE can use the decay formula

Aₓ = A₀e^-(ln2/t1/2)t
1,000,000(1/16) = (1,000,000)e^-(ln2/5750)t
t = 23,000 years