Carbon-14 is produced in the atmosphere when neutrons from cosmic radiation react with nitrogen atoms: C ratio of 0.795 times that found in plants living today. 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: 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. As soon as a living organism dies, it stops taking in new carbon.
Libby and coworkers, and it has provided a way to determine the ages of different materials in archeology, geology, geophysics, and other branches of science.
Some examples of the types of material that radiocarbon can determine the ages of are wood, charcoal, marine and freshwater shell, bone and antler, and peat and organic-bearing sediments.
By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely. So, if you had a fossil that had 10 percent carbon-14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (-0.693) ] x 5,700 years t = [ (-2.303) / (-0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old.
However, the principle of carbon-14 dating applies to other isotopes as well.
Potassium-40 is another radioactive element naturally found in your body and has a half-life of 1.3 billion years.
Other useful radioisotopes for radioactive dating include Uranium -235 (half-life = 704 million years), Uranium -238 (half-life = 4.5 billion years), Thorium-232 (half-life = 14 billion years) and Rubidium-87 (half-life = 49 billion years).When these energetic neutrons collide with a nitrogen-14 (seven protons, seven neutrons) atom it turns into a carbon-14 atom (six protons, eight neutrons) and a hydrogen atom (one proton, zero neutrons).Since Nitrogen gas makes up about 78 percent of the Earth's air, by volume, a considerable amount of Carbon-14 is produced.Anything that dies after the 1940s, when Nuclear bombs, nuclear reactors and open-air nuclear tests started changing things, will be harder to date precisely. Climate records from a Japanese lake are set to improve the accuracy of the dating technique, which could help to shed light on archaeological mysteries such as why Neanderthals became extinct.But even he “realized that there probably would be variation”, says Christopher Bronk Ramsey, a geochronologist at the University of Oxford, UK, who led the latest work, published today in Science.