Radiocarbon Dating

Detailed information
Detailed information about the method of radiocarbon dating, the active laboratories and the literature  is available on the Radiocarbon website.

Equilibrium ratio
Radiocarbon dating is based on the presence of the an equilibrium ratio of R(0) = ¹⁴C/¹²C in the carbon cycle. Organisms take up carbon during their life and so obtain the equilibrium value from the environment. During the growth the carbon and its ratio becomes fixed in cells of plants, animals and humans. After the death of the organism the exchange with the environment stops and also the uptake of ¹⁴C. Because of the decay of ¹⁴C, the  ¹⁴C/¹²C ratio decreases according to R(t)=R(0) exp(-t/t_1/2), where t_1/2 is the half life. So, the ratio R(t) is  a measure for the age of the material.

Reservoir age
The equilibrium ratio is not everywhere the same on earth. This causes apparent age differences, known as reservoir ages. In a marine environment, the average reservoir age is 400 years, because of the dissolution of old carbonates from sediment. Such reservoir ages can also be present in lakes, rivers and other carbonates. Other complications exist, which are connected with the possibility to select the correct chemical fraction without contamination (see material).

Radiocarbon age
The time past since death is derived from the measured ratio R(t)  with t = - 8033 ln [R(t)/R(0)]. The uncertainty Dt of the age t depends on the uncertainty of R(t) through Dt = 8033 DR/R, which shows that an 1% uncertainty in R results in an 80 year uncertainty of age. Although the carbon dioxide mixes well in the atmosphere  variations in the equilibrium value R(0) occur. are not taken into account. To correct for these a calibration curve is used which is based on the ¹⁴C-ages of tree-rings of known calendar age as identified from dendrochronology.

Calibration to calendar years
Calibration of the interval spanned by the ¹⁴C-age and its uncertainty to a corresponding interval can result in one or more valid intervals. This depends on the smoothness of a calibration curve. For example, ¹⁴C dates from the period after 1660 AD cannot be discriminated against modern material, as is shown in the figure. Various calibration programs are available to calculate the calendar age interval from the ¹⁴C date.

The ¹⁴C bomb peak
Nuclear weapon testing in the atmosphere caused in the 1960's almost a doubling of the  ¹⁴C activity in the atmosphere. After the stop of these nuclear tests in the atmosphere the peak started to decrease through interaction of the atmosphere with the other carbon reservoirs. The ¹⁴C data showing the bomb peak on the northern and southern hemisphere reflect the exchange between both hemispheres nicely. The rise of the peak on the northern hemisphere, where the tests were made, is only a year earlier than on the southern hemisphere.  Clearly, the ¹⁴C-bomb peak in both hemispheres can be used to retrieve very precise dates in this period.