This means that a living plant or animal has only one Carbon 14 atom for every trillion Carbon 12 atoms. C-14 is formed when cosmic rays knock neutrons out of carbon atoms in the Earth's upper atmosphere. Some of these neutrons hit Nitrogen-14 nuclei, causing a proton to be ejected, and converting them to C-14. In a process called photosynthesis, plants use the energy in sunlight to convert carbon dioxide from the atmosphere into carbon-bearing compounds that the plant can utilize. This process continues as long as the plants are alive. Some animals eat plants and use the carbon in the food to help them grow. Some animals eat other animals, and similarly use the carbon that they ingest. Because of the flow of carbon along the food chain, the ratio of C-14 to C-12 in living matter remains approximately the same as the ratio in the atmosphere while the plant or animal lived. In the case of flax, it progresses from seed, to adult plant, to cultivation in a matter of months. There is no opportunity for a significant percentage of C-14 to decay while the flax is alive. C-14 decay only becomes significant in the ongoing centuries after the plant dies. As an initial working hypothesis, one might assume that the ratio of Carbon 14 to Carbon 12 has been constant through the past 50,000 years. After the plant or animal dies, no more carbon is ingested from the environment. Individual C-14 atoms decay by changing back into N-14, a stable form of Nitrogen. After 5,730 years, only half of the original C-14 is left. After another 5,730 years, only a quarter of the original amount it is left; after another 5,730 years, only one eighth is left. The term "half-life" ("t 1/2") refers to the time taken for half of the atoms to decay. C-14's half life is 5,730 years Â~+mn~40 years. Thus by measuring the ratio of Carbon 14 to Carbon 12 in the sample, one can estimate the number of years before the present time ("BP") when the plant or animal died. Libby and his team computed the theoretical ratio of C-14 to C-12 that they expected for various ages of objects, subject to the assumption that the ratio in the atmosphere has always been constant. They then tested the C-14 dating technique on a number of carbon-bearing samples from ancient Egypt whose age was already precisely known. The ancient Egyptians had a calendar with some known peculiarities that has enabled archeologists to translate dates from the Egyptian calendar to our own. For example, they obtained a sample of wood from Pharaoh Zoser's tomb which was part of a living tree circa 2600 BCE. The agreement between the theoretical curve and the actual results was very close. "Each result was within the statistical range of the true historic date of each sample:" 1 They also counted annual growth rings in some 1000 to 1500 year old tree samples to precisely determine their age. Their initial calibration curve is shown below. Additional points have been determined to confirm that the theoretical curve is accurate beyond 10,000 years before the present.
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