As soon as a living organism dies, it stops taking in new carbon. The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but after death, the carbon-14 that decays is not replaced.
The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample. 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.
A formula to calculate the conventional radiocarbon age (CRA) of a given sample is by carbon-14 dating is:
t = [ ln (Nf/No) / (-0.693) ] x t1/2
where:
- ln is the natural logarithm
- Nf/No is the percent of carbon-14 in the sample compared to the amount in living tissue
- t1/2 is the Libby half-life of carbon-14 (5,700 years)
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
t = 18,940 years old
Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating organic matter 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). The use of various radioisotopes allows the dating of biological and geological samples with a high degree of accuracy.
However, radioisotope dating may not work so well in the future. Anything that dies after the 1940s, when nuclear weapons, nuclear reactors, atmospheric testing and burning fossil fuels started to alter carbon ratios, will be harder to date precisely.
