Derivation of Formula for the Calculation of Radiocarbon Dating

Radio carbon dating

 A radio carbon or carbon -14, ¹⁴C,  is a radioactive  isotope of carbon, it is formed in the atmosphere as a result of collision between cosmic rays and nucleus of atoms. Radiocarbon is produced by the reaction of neutron with nitrogen in the air. The radiocarbon created combine with atmospheric oxygen to form radioactive carbon(iv)oxide .  As shown by the equation below

¹⁴N + n = ¹⁴N + p    where n and p are neutron and proton respectively

¹⁴N   = ¹⁴N + _-β

In the atmosphere also there are carbon -12 isotope which is not radioactive therefore non-radioactive carbon(iv)oxide are also formed in the atmosphere.

 This radioactive carbon are absorbed by plant during the process of photosynthesis, likewise herbivore animals that feed on this plant will absorb and carnivores animal that feed on this herbivores will also have this radiocarbon in their body.

When this animal or plant dies the intake of carbon-14 stops and therefore exchange of materials with its environment stops , the level of radiocarbon continue to decrease by half every 5730 years .

By determining the proportion of radiocarbon to ordinary carbon in their remains( bones, wood, skull etc.),  it is possible to evaluate the ages of the ancient object of organic origins. With this method oldest dates up to about 50, 000 years can be measured.

Measuring carbon-14 from a sample can be done using beta counting devices, or an accelerator mass spectrometer is used, the second device can count all radiocarbon atom in the sample.

Also check derivation of equation for rock ages