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1. What is the basis of carbon-14 dating?
Carbon exists in three forms, or isotopes, carbon-12 (12C), carbon-13 (13C), and carbon-14 (14C). Carbon-14 is formed in the upper atmosphere when a neutron in cosmic radiation strikes an atom of nitrogen-14 (14N) and converts it to carbon-14.  The 14C is unstable (radioactive) and eventually decays  back to nitrogen-14. The rate of decay is such that half the atoms of carbon-14 in a sample decay to nitrogen in approximately 5730 years.  When the rates of 14C formation and decay reach equilibrium, the concentration of 14C in the atmosphere reaches a constant level. The modern level is about 1 atom of 14C in every trillion carbon atoms.  The constant decay rate allows scientists to calculate the time required for the 14C level in a sample to reach a given concentration.
Living organisms take in carbon, in the form of carbon dioxide, through their food and water, thus maintaining the same level of 14C in their bodies as is in their environment. When organisms die, the 14C in their bodies is no longer replaced, so the level of 14C declines as it decays to 14N. The longer the time since death, the more of the 14C will have decayed, so the less 14C remains in the body. Scientists can measure the concentration of 14C in a sample with a high degree of accuracy and then calculate how long it would take for the concentration of 14C in the sample to decline from an assumed starting level to the level measured in the sample. This is the (uncorrected) carbon-14 age of the sample. 
Usually the raw carbon-14 age of a sample is not thought to be the actual age. In practice, the level of 14C in a sample is compared to a standard calibration curve constructed by measuring the 14C present in samples of known age.  The standard calibration curve deviates significantly from the dates arrived at by assuming knowledge of initial 14C concentrations and a constant decay rate.
2. What materials can be dated by carbon-14?
Carbon-14 is used to date materials that were once living and still contain measurable amounts of 14C atoms. It is widely used in dating fossils or archaeological samples containing organic material such as wood, charcoal, bone, shells, etc. It is not used to date rocks or other inorganic material.
Carbon-14 dating cannot be applied to materials that have no 14C. Most limestone, diamonds, coal and oil are expected to have no residual 14C because of their presumed age,  so they are not usually used in radiocarbon dating. After approximately ten half-lives, the amount of 14C becomes so small it is difficult to measure. Ten half-lives of 14C makes about 57,300 years, so most 14C dates are less than that figure. It is sometimes thought possible to extend the dating range a few half-lives, so one occasionally sees dates as old as 70,000 years or more. Carbon-14 dating does not produce ages in the millions of years, as do some other types of radioisotope dating. 
3. How accurate are carbon-14 dates?
The experimental part of 14C dating consists of measuring the amounts of carbon-14 and carbon-12, and sometimes C-13, in a sample. This can be done very accurately, although some samples may be difficult to work with. Beyond this, the accuracy of the date depends on the reliability of the assumptions used in interpreting the measurements (see below).
Carbon-14 dates usually appear to be reasonably accurate whenever they can be checked against historical records. For example, when the Dead Sea Scrolls were dated, three methods could be used: 1) Dates written in the documents themselves (like the date at the start of a letter) 2) Paleography, which uses the style of script used to write documents to date them, and 3) Carbon-14. In most cases, the three methods produced similar results. Surprisingly, in at least one case the date range given by 14C dating did not coincide with the internal date in the document. 
Radiocarbon dating sometimes produces anomalous results, such as when organisms do not take in ordinary amounts of 14C, but these are often easily explained. Before about 1500 B.C., historical records are few, and tree-ring counts have been used to calibrate and correct raw 14C dates. The resulting standard calibration curve has some wobbles in which the same 14C concentrations are found in samples of different ages. Samples corresponding to these parts of the curve may yield multiple dates. 
4. What are the assumptions used in determining carbon-14 dates?
Calculating a date based on the concentration of radiocarbon in a sample is based on several assumptions. The first assumption is that the decay rate of 14C has not changed over time. Recently some evidence has been published in peer-reviewed journals suggesting that this assumption may not be true for all isotopes. While 14C has not been observed to vary, the rates of Silicon-32 and Radium-226 decay may vary in relation to Earth’s distance from the sun.  There may be other examples of systematic variation in isotope decay rates. While the small variations in isotope decay that have been reported may not invalidate all isotopic dating, they raise questions about the assumption of completely uniform decay rates.
A second assumption is that the sample being dated has not experienced any loss or contamination of 14C over its history. The reasonableness of this assumption probably depends on the environment around the sample. A sample that is sealed from the surrounding environment is more likely to avoid contamination or loss than one in an open environment where materials may be carried into or out of the sample by water or simple diffusion. Violations of this assumption can frequently be identified.
Three additional assumptions are necessary in radiocarbon dating in order to estimate the initial concentration of 14C in the environment during the time when the organism providing the sample lived.  The concentration of carbon-14 production in the lower atmosphere must have been relatively constant. This depends on the rate at which 14C is produced in the upper atmosphere and the evenness of its mixing in the lower atmosphere. Variations in production of 14C could be caused by changes in the intensity of the cosmic radiation or in the strength of the earth’s magnetic field. It is known that such variations have occurred, but it is thought they can be corrected for by comparing a sample’s 14C level with the standard curve constructed using samples of known age.
Another assumption is that the amounts of carbon-14 present in the geophysical reservoirs must be constant. The geophysical reservoirs include the atmosphere, the oceans, the biosphere, and the sediments. Violations of this assumption occur in the ocean reservoir due to the time required for mixing of surface waters with the deep layers. Violations in the atmosphere result from volcanic eruptions that occasionally add 12C to the system, thus diluting the 14C present. In recent times, above-ground atomic tests have also changed the atmospheric concentration of 14C. Also, there is a lag time for atmospheric mixing in the northern and southern hemispheres which results in somewhat different ages for the two hemispheres. Other processes may affect the local concentrations of carbon-14.  These effects are corrected for by comparing samples from different locations. A final assumption is that the various rates of flow of carbon-14 among the respective geophysical reservoirs must be constant, and the residence time of carbon-14 in the various reservoirs must be short relative to its half-life.
If these three conditions are met, the initial concentration of 14C in the sample can be estimated. In practice, there are sufficient variations in these conditions that it is necessary to correct a sample’s raw radiocarbon age by comparing it with the standard calibration curve.
5. How would carbon-14 dating be affected by a global flood?
Carbon-14 dating depends on the amount of atmospheric carbon-14 relative to carbon-12. This ratio would have been different before the Flood. The earth’s sediments contain a vast amount of carbon-12 in the form of coal and oil.  The amount of 14C in coal and oil is much less than in the present environment. If a significant portion of the coal and oil represents organisms that were deposited in a global flood, then the pre-flood atmosphere must have contained much less 14C and more 12C than the present atmosphere. If the rate of production of 14C were no greater before the flood than it is now, the pre-flood 14C would have been greatly diluted by the vast amount of pre-flood 12C. This would cause any pre-flood organic material to have a 14C date much older than the actual calendar date. After the flood, a new equilibrium concentration of 14C would be established over a period of time.  Plants and animals that lived during the time when the new equilibrium was being established would show old 14C ages, converging on calendar time over a period approximating a thousand years. 
6. What unsolved problems about carbon-14 dating are of greatest interest?
What are the actual causes of fluctuations in 14C over time resulting in wobbles and deviation from expected levels in the standard calibration curve based on samples of known age? Why do ancient samples of coal, diamonds and other carbon-containing materials consistently contain 14C at levels yielding dates older than the Bible allows for and yet much younger than conventional geology suggests?
 More specifically, the neutron is captured by a 14N atom, converting it to 15N, an unstable isotope with 7 protons and 8 neutrons. Nitrogen-15 decays to carbon-14 by ejecting one of its protons, leaving a carbon nucleus with 6 protons and 8 neutrons.
 One of the 14C neutrons decays to a proton and an electron. The electron is emitted as a beta particle, leaving a 14N nucleus with 7 protons and 7 neutrons.
 See Godin, H. Half-life of radiocarbon. Nature 195(1962):984.
 The method is more fully described in various references such as: Newcomb RC. 1990. Absolute Age Determination, (Berlin and NY: Springer-Verlag, 1990), 162-180.
 The first such curve was published by: Arnold, JR and WF Libby. Age determinations by radiocarbon content: Checks with samples of known age. Science 110(1949):678-680. Subsequent revisions have been made, e.g., Reimer, PJ et al. IntCal09 and Marine09 radiocarbon age calibration curves, 0-50,000 years cal BP. Radiocarbon 51(4, 2009):1111-1150.
 Actually, small amounts of 14C have been reported from coal. E.g., see Lowe, DC. Problems associated with the use of coal as a source of 14C-free background material. Radiocarbon 31(2, 1989):117-120;
 This was the scroll “Testament of Qahat,” for which the radiocarbon date was about two centuries older than the date based on paleography. See Bonani, G. et al. Radiocarbon dating of fourteen Dead Sea Scrolls. Radiocarbon 34(1992):843-849.
 Note the wobbles in the curves in Pearson, GW et al. High-precision (super 14C measurement of Irish oaks to show the natural 14C variations from AD 1840 to 5210 BC. Radiocarbon 28(2B, 1986):911-938.
 Jenkins JH, Fischbach E, Buncher JB, Gruenwald JT, Krause DE, Mattes JJ. Evidence for correlations between nuclear decay rates and Earth-Sun distance - et al. Astroparticle Physics 32(2009):42-46. arXiv:0808.3283. DOI 10.1016/j.astropartphys.2009.05.004.
 Taylor, RE. 1987. Radiocarbon Dating: An Archaeological Perspective. (New York:NY: Academic Books, 1987), 3.
 Taylor, op cit, p 126-132.
 Post WM, Peng TH, Emanuel WR, King AW, Dale VH, Deangelis DL. The global carbon cycle. American Scientist 78(4, 1990):310-326. According to these authors, the total mobile (non-carbonate) carbon in the biosphere is about 40,000-45,000 gigatons. The amount of carbon in fossil fuels is estimated at 6,000 gigatons, and the amount of kerogens (organic) in sediments is about 15 million gigatons. This gives a ratio of 300:1 for pre-Flood biosphere carbon to present biosphere carbon. This differs by a factor of only two from the figure of 143:1 proposed by Brown (Brown, RH. The upper limit of C-14 age? Origins 15(1988):39-43). See also Falkowski, P. et al. The global carbon cycle: a test of our knowledge of Earth as a system. Science 290(2000):291-296.
 Brown, RH. The interpretation of C-14 dates. Origins 6(1979):30-44; Giem, P. Scientific Theology. (Riverside, CA: La Sierra University Press, 1997), 183. Giem, P. Carbon-14 dating models and experimental implications. Origins 24(2, 1997):50-64
 The deep ocean waters are estimated to take about 1000 years to circulate back to the surface: Aitken, MJ. Science-based Dating in Archaeology. (Harlow, Essex, England: Longman House, 1990), 64.