Question

1. 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

There are two ways to solve this problem. The easier one is to use your understanding of what a half-live is and use that to figure out how much time (how many half-lives) have passed to have remaining 1/16 of the original sample.

Knowing that a "half-life" is the amount of time for half of a sample to decay - into whatever else, we can construct a table. After one half-life has passed only 1/2 of the original sample remains, after another half-life (two half-lives in total) 1/4 of the original sample remains. The pattern is such that you divide the remaining sample by 2 each half-life that passes.



With this table you can "Determine approximately how many years ago the tree was chopped down to be used for the firewood."

Multiply the number of half-lives by the half-life of C-14 (5,750 years)

For "If you started with 1 million carbon-14 atoms, how many atoms would remain in the wood?" you only need to find 1/16 of 1 million.