C-14 Analysis
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The basis of this methodology is the production of the radioactive isotope carbon 14 (C-14) through the interaction of nitrogen with neutrons produced by cosmic radiation. The collision of a neutron with a nitrogen-14 nucleus can produce a carbon-14 atom and a hydrogen atom.

1
0

14
7

14
6

1
1
n +  C +  H

Regular carbon atoms, C-12, contain six neutrons in the nucleus. Radiocarbon, an unstable form of carbon, has eight neutrons in the nucleus. Due to the constant production of C-14 and its radioactive decay a small, relatively constant fractional quantity of C-14 exists in the atmosphere. Living organisms maintain equilibrium with C-14 in the atmosphere. They absorb C-14, which remains detectable after their death. Before 1000 BCE the levels of C-14 were a bit higher than they are now. The burning of fossil fuels and the atmospheric testing of nuclear weapons has affected the fraction of C-14 in present-day atmospheric CO2

These organisms replace C-14 atoms that have undergone radioactive decay, at a present day rate of 15.3 disintegrations per minute per gram of total carbon, with fresh C-14 atoms by absorption. The fact that an organism no longer absorbs C-14 from the point of death allows a precise determination of the amount of C-14 remaining in the organism. This requires adequate samples and sufficiently sophisticated sensitive and calibrated equipment. The remaining C-14 disintegrates at a constant rate known as a half-life as follows:

14
6

14
7

0
-1
N +  e

Its half-life refers to the amount of time it takes for the rate of particle emission to decrease by one-half of its existing level through decay. Since C-14 has a half-life (t1/2) of 5,730 years the amount of radiocarbon remaining active establishes the elapsed time. Researchers establish the age of a dead organic object by measuring the level of beta emissions arising from the radioactive decay of C-14 in the object and calculating how long it took for C-14 to decay from its point of death to account for the level of beta emissions measured.

Dating a Sample Using C14 Analysis

A sample of a living organism emits 15 particles per second. The same size sample of organic material found in an excavation emits 3.75 particles per second. What is the age of the sample BP and what was its age when first analyzed in 1993?

  1. The half-life of C14 is 5,730 years. t1/2 = 5730

  2. Since 3.75 particles per second are given in 1993 the half-life producing this result took 5,730 years.

  3. Thus 5,730 years before 1993 the sample would have emitted 7.50 particles per second (2 X 3.75).

  4. An additional full half-life would result in the organism emitting 15 particles per second (2 X 7.50 particles per second). This brings the age of the sample to 11,460 years (5,730 + 5,730).

  5. Assuming a constant rate of decay the sample lived 11,460 years before 1993 since at that time it would have emitted 15 particles per second.

  6. It should be dated to 11,417 BP (1993 - 1950 = 43 11,460 - 43 = 11,417)

  7. Also it can be dated to BCE 9423 [1993 - 11,417 + 1 (since there is no year 0) = 9423]

Calibration issues accompany radiocarbon dating for the rate of production of C-14 has not always been a constant with sampling concerns and the sophistication of instrumentation remaining additional factors. Improved sampling techniques, new and improved instrumentation requiring smaller quantities of organic material for analysis, and the use of dendrochronology for calibration have reduced the standard error of measurement in radiocarbon dating.

One can determine the date of an organic sample using the following equation: 

log Nt - log N0 =

 

  -kt  
2.303

N0 is the original number of C-14 nuclei in the original sample (t = 0). After a period of time t, the number of nuclei decreases by decay to the number Nt is the number of C-14 nuclei in the same sample after elapsed time t. The fraction of nuclei remaining after elapsed time t is Nt/N0. where k = 0.693/t1/2 and t1/2 = 5730 years

t = (2.303 t1/2 divided by 0.693)(log N0 - log Nt)

Interestingly, in the Levant, calibrated dates in the fourth and third millennia BCE appear too early when compared to dates derived through accepted Egyptian chronology by means of pottery analysis. From 3,000 BCE, the absolute chronology of the Levant relies upon a correlation with Egyptian chronology. This coincides with the import and export of objects. This high dependence on Egyptian chronology requires any change in Egyptian chronology necessitating a parallel change concerning the chronology of the Levant. If the calibrated radiocarbon dates stand then revision in the accepted Egyptian chronology may soon follow.


Page last edited: 01/25/06 07:11 PM


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