Question

Carbon-14 dating assumes that the carbon dioxide on earth today has the same radioactive content as it did centuries ago. if this is true, the amount of 14c absorbed by a tree that grew several centuries ago should be the same as the amount of 14c absorbed by a tree growing today. a piece of ancient charcoal contains only 20% as much of the radioactive carbon as a piece of modern charcoal. how long ago was the tree burned to make the ancient charcoal? (the half-life of 14c is 5715 years. round to the nearest year.)

Answer 1

Half-life is a first-order reaction which means the rate of decay is constant. Using the supplied value of the half-life of 14c (5715 years), and that the piece of ancient charcoal contains only 20% as much of the radioactive carbon as a piece of modern charcoal, the calculated "age" or timespan when the tree got burned is 13269.819062281 or simply, 13270 years ago.