How Carbon-14 Is Used To Date Artifacts

How Carbon-14 Is Used To Date Artifacts In the 1950s W.F. Libby and others (University of Chicago) devised a method of estimating the age of organic material based on the decay rate of carbon-14. Carbon-14 dating can be used on objects ranging from a few hundred years old to 50,000 years old. What Is Carbon-14? Carbon-14 is produced in the atmosphere when neutrons from cosmic radiation react with nitrogen atoms: 147N 10n → 146C 11H Free carbon, including the carbon-14 produced in this reaction, can react to form carbon dioxide, a component of air. Atmospheric carbon dioxide, CO2, has a steady-state concentration of about one atom of carbon-14 per every 1012 atoms of carbon-12. Living plants and animals that eat plants (like people) take in carbon dioxide and have the same 14C/12C ratio as the atmosphere. However, when a plant or animal dies, it stops taking in carbon as food or air. The radioactive decay of the carbon that is already present starts to change the ratio of 14C/12C. By measuring how much the ratio is lowered, it is possible to make an estimate of how much time has passed since the plant or animal lived. The decay of carbon-14 is: 146C → 147N 0-1e (half-life is 5720 years) Example Problem A scrap of paper taken from the Dead Sea Scrolls was found to have a 14C/12C ratio of 0.795 times that found in plants living today. Estimate the age of the scroll. Solution The half-life of carbon-14 is known to be 5720 years.​ Radioactive decay is a first order rate process, which means the reaction proceeds according to the following equation: log10 X0/X kt / 2.30 where X0 is the quantity of radioactive material at time zero, X is the amount remaining after time t, and k is the first order rate constant, which is a characteristic of the isotope undergoing decay. Decay rates are usually expressed in terms of their half-life instead of the first order rate constant, where k 0.693 / t1/2 so for this problem: k 0.693 / 5720 years 1.21 x 10-4/year log X0 / X [(1.21 x 10-4/year] x t] / 2.30 X 0.795 X0, so log X0 / X log 1.000/0.795 log 1.26 0.100 therefore, 0.100 [(1.21 x 10-4/year) x t] / 2.30 t 1900 years