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Radiocarbon dating method has been developed from the study of influence of cosmic irradiation to the Earth and its atmosphere. Radioactive isotope of carbon (radiocarbon, 14C) is created in upper layers of the atmosphere by the capture of a cosmic-ray produced neutron on nitrogen in the reaction:
14N + n → p + 14C
The 14C is then oxidized to 14CO2 and distributed evenly throughout the global atmosphere. The concentration ratio of carbon isotopes 12C : 13C : 14C is almost the same in the whole atmosphere and it is 1012 : 1010 : 1. Only the isotope 14C is radioactive, so the nuclei decay according to the reaction:
14C → 14N + β- + ν
The reaction energy is 156 keV.
Since the desintegrated 14C atoms are replaced by those formed in the atmosphere, where the production is constant for millenia, the specific activity of 14C in the nature and living organisms remains constant. Natural specific activity in atmospheric CO2 , in ocean carbon and in living organisims (plants, animals, humans) is:
A0=(13.56±0.70) dpm/g carbon
or
A0=(0.226±0.012) Bq/g carbon,
and in air 0.037 Bq/m3 =1.0810-12 Ci/m3, because 1 m3 of air contains 0.177 g carbon at normal conditions.
The total activity of 14C at the Earth is estimated to be 140·1015 Bq.
Plants assimilate 14C during photosynthesis, and animal eat plants. Thus, all living terrestrial creatures maintain their 14C input during the life. 14CO2, like normal CO2, dissolves in the oceans and is available to plankton, corals, molluscs and fish, so all creatures during their life continuously replenish their 14C content. At death of organisms 14C input ceases and the amount of 14C in organic matter decreases according to the exponential law of radioactive decay:
A = A0 · e-λt
where A0 is the concentration of 14C activity in the organism in the moment of death and A in the moment of measurement, i.e. after the time t elapsed from the moment when the sample was removed from the dynamic reservoir of carbon. The letter λ denotes the radioactive constant for 14C:
λ = ln2 / T1/2
where T1/2 is the half life of 14C (T1/2 = 5730 years). The age of sample is then expressed by relation:
t = 1/λ · ln( A0/A) = 8033 · ln( A0/A)
By convention, the 14C age is expressed in years BP (Before P resent), where for the start year 1950 is taken. Also by convention, the "old", so-called Libby radiocarbon half-life of 5560 years is taken for 14C age calculation.
Fig. 1: Decay of 14C during the time t elapsed from the death of organism
The result can be expressed as the percentage of the natural specific activity in the atmosphere (A0) as:
a14C = A/A0 · 100 pMC
(pMC= percent of modern carbon). Deviations of the measured activity from the natural activity are expressed by so called δ-values:
δ14C = (A-A0)/A0 · 1000 ‰
Samples suitable for 14C dating are primarily those containing organic carbon: wood, charcoal, peat, organic mud, bones, leather, hair, horns, organic soil, wheat etc. Carbonates containing carbon that is a part of the natural cycle can be dated too: shells, carbonate sediments, as speleothems (stalactites, stalagmites), tufa, lake sediments, as well as dissolved carbon (bicarbonates) in water.
There are several factors that influence the accuracy of 14C dating: (a) the isotope exchange process, i.e. fractionation of carbon atoms, (b) past variation of 14C concentration activity in the atmosphere, as well as (c) contamination of samples with recent or old 14C.
Measurement of 14C activity requires very sensitive techniques: gas proportional counters (GPC), liquid scintillation counters (LSC) or accelerator mass spectroscopy (AMS). The maximal age which can be measured by GPC is about 40,000 years, by LSC 50,000 years and by AMS more than 60,000 years. The amount of carbon measured by GPC and LSC techniques should be at least several grams, while by the AMS method miligram-sized samples can be measured.
The main international journal for research papers and data lists relevant to 14C problematic is RADIOCARBON. More information about radiocarbon dating can be found on Radiocarbon WEB info pages.
