Carbon dating

The carbon dating is a radiometric method of Datation based to the measure of the radiological activity of the Carbon-14 contained in Organic matter which one wishes to know the absolute age, namely the time passed since its death.

The field of application of this method corresponds to absolute ages of a few hundred years until approximately 50.000 years. The application of this method to old events, particularly when their age exceeds 6.000 years (prehistoric), made it possible to date them much more precisely than before. It thus brought a significant progress in Archéologie and Paléoanthropologie.

History

In 1960, Willard Frank Libby received the Nobel Prize of chemistry for the development of this method (cf article on the researcher for the history of this discovery).

Principle of the dating

The Carbon-14 (¹⁴C) or radiocarbon is a radioactive Isotope of the Carbone whose radioactive Half-life (or half-life) is equal to 5.730 years.

A living organism assimilates carbon without isotopic distinction. During its life, the proportion of ¹⁴C present in the organization compared to carbon total (¹²C, ¹³C and ¹⁴C) is same as that existing in the atmosphere of the moment.

The carbon dating is based thus on the presence in any radiocarbon organization in negligible proportion (about 10^-12 for the total ¹⁴C/C report/ratio). As from the moment when an organization dies, the quantity of radiocarbon which it contains as its radiological activity decrease during time according to an exponential law. An organic matter sample resulting from this organization can thus be dated by measuring either the total ¹⁴C/C report/ratio with a Mass spectrometer, or its activity X years after the death of the organization.

Origin of natural radiocarbon

Natural radiocarbon circulates in three tanks: the atmosphere, the Ocean S and the Biosphere.

With a radioactive Half-life 5.730 years, radiocarbon would for a long time have disappeared from the Biosphère if it were not produced permanently.

In the upper atmosphere, nuclear reactions with the Proton S of the cosmic radiation produce Neutron S. After being slowed down by collision with the Molécule S of the air, the neutrons react with the Azote to form radiocarbon:

$\ mathrm {N} + ^ {14} \! \ mathrm {NR} \ rightarrow ^ {14} \! \ mathrm {C} + ^ {1} \! \ mathrm {H}$

This reaction is privileged owing to the fact that the Azote constitutes 78,11% of the atmosphere of the ground. It is between 7000 meters and 12.000 meters that the production of radiocarbon takes place.

Radiocarbon reacts quickly with the Oxygène to form Carbon dioxide. This Gaz circulates in all the atmosphere and dissolves in the oceans to form Carbonate S. Of radiocarbon thus circulates also in the oceans.

Carbon dioxide also reacts with the Biosphère. The plants assimilate radiocarbon in the atmosphere by Photosynthèse and they are eaten by the animals. The marine organizations also assimilate radiocarbon present in the oceans. Radiocarbon is thus spread in the Biosphère throughout the Food chain.

The total ¹⁴C/C relationship is regarded as uniform in the atmosphere, the surface of the oceans and the biosphere because of the permanent exchanges between the living organisms and their medium.

Moreover, one supposes that the Flux of cosmic rays is constant over one long period of time (first approximation). Consequently, the production rate of radiocarbon is constant, therefore the total ¹⁴C/C report/ratio in the atmosphere, the surface of the oceans and the biosphere is constant (the number of produced atoms equalizes the number of atoms which disintegrates).

With died of an organization, any exchange with the external medium ceases but radiocarbon remains trapped and its quantity starts to decrease exponentially according to the process of the radioactive decrease: this makes it possible to know since how long the organization died.

Measure age of an organic matter sample

The radioactive decay of carbon-14 obeys a law of exponential decay characterized by its half-life. To go back a sample to organic matter consists in measuring the total ¹⁴C/C report/ratio (what remains of natural radiocarbon following disintegration) and deducing its age from it. The total ¹⁴C/C report/ratio is measured either indirectly by the measurement of the specific activity (many disintegrations per unit of time and unit of carbon mass) due to the natural radiocarbon which is proportional to the total ¹⁴C/C report/ratio, or directly by Spectrometry mass.

When it was developed by Libby at the end of the years 1940, the carbon dating passed by the measurement of the radioactivity of the samples what was delicate because of weakness of the signal (there are few radiocarbon atoms in the sample analyzed, especially after a few thousands of years, and even less which disintegrate) and of the background noise (natural radioactivity, cosmic rays…)

Today, the direct measurement of the total ¹⁴C/C report/ratio by Spectrometry mass is privileged because it makes it possible to date from the samples much smaller (less than one milligram compared with several grams of carbon before) and much more quickly (in less than one hour against several days or weeks). The carbon extracted the sample is initially transformed into Graphite, then in Ion S which is accelerated by the tension generated by a mass spectrometer coupled to a Particle accelerator . The various isotopes of carbon are separate thanks to a Aimant what makes it possible to count the carbon-14 ions.

The old samples of more than 50.000 years cannot be dated with carbon-14 because the total ¹⁴C/C report/ratio is too weak to be measured by the current techniques; the results are relatively precise only for the ages lower than 35.000 years

The most current method of dating consists in determining the concentration ${C} _ {T}$ of radiocarbon (i.e. the total ¹⁴C/C report/ratio) of one sample at the moment $t$ of measurement; the age of the sample is then given by the formula:

{T} - = \ frac {1} {\ lambda} \ times \ ln \ frac

where

{C} _0

is the radiocarbon concentration of the sample at the moment

{T} _0

of died of the organization from which the sample comes (

{C} _0 \ approx10^ {- 12} \

) and

\ lambda

the decay constant of carbon-14 (

\ lambda= \ frac {\ ln2} {t_ {\ frac {1} {2}}} \ approx1,210 \ cdot10^ {- 4} \ \ mathrm {years} ^ {- 1}

Conventional radioactive half-life

The age conventional carbon-14 of an organic matter sample is calculated as from one 5.568 years conventional period, calculated in 1950 starting from series of measure. Since, more precise measurements were carried out, and give one 5.730 years period but the laboratories continue to use the conventional value to avoid confusions.

The results are given in years “before present” (BP). Item zero (from which time passed since the death of the organization is measured from which this matter is resulting) is fixed at 1950, by supposing a radiocarbon level equal to that of 1950 because since pollution largely the atmospheric rate of carbon dioxide modified!

Calibration curves

With the beginning of the year 1960, certain systematic divergences observed between the age of samples estimated by the carbon dating and the Archeology or the Dendrochronologie pose problem.

Even if the flow of cosmic rays at the origin of the formation of the ¹⁴C can be presumedly constant, space research highlighted that the quantity of this flow received in the high terrestrial atmosphere varied following the evolutions of the Terrestrial magnetic field and of the solar magnetic field. This explains why the production rate of natural radiocarbon varied during time.

The climate changes as well as the fossil carbon massive rejection in the atmosphere by industry and transport also modified the total quantity of carbon in the three tanks (atmosphere, oceans and biosphere). Lastly, during the years 1950 and 1960, the nuclear tests almost doubled the quantity of radiocarbon in the atmosphere. However these recent phenomena do not have impact on the dating of old objects, whose ¹⁴C/C report/ratio depends only on their age, and of the rate ¹⁴C/C at the date of their stop of biological activity.

In conclusion, the total ¹⁴C/C report/ratio in the biosphere is not constant in time. It is thus necessary to build curves of calibration by confronting the datings obtained thanks to carbon-14 and the datings by other methods such as the Dendrochronologie.

These curves allow, knowing the age conventional carbon-14 of a sample, to find the date corresponding in our Calendrier.

Other corrections

The vehicles been driven by internal combustion engines use oil products which contain only stable isotopes of carbon, ¹²C and ¹³C; the totality of carbon-14 having disappeared during the long life from hiding from fossile fuels.

It will be also the case of carbonaceous gases rejected by these vehicles; thus, the dating with the ¹⁴C of a shrub pushing in edge of the highways will be able to frequently allot to him a twelve thousand years age or more.

Tables of correction thus exist to allow datings related to the industrial revolution, according to the places of gas emissions carbonaceous deprived in ¹⁴C, resulting from fossile fuels.

See too

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