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The Art and Science of Modeling with First-Order Equations
Published in Kenneth B. Howell, Ordinary Differential Equations, 2019
(Carbon-14 dating) A little background:Most of the carbon in living tissue comes, directly or indirectly, from the carbon dioxide in the air. A tiny fraction (about one part per trillion) of this carbon is the radioactive isotope carbon-14 (which has a half-life of approximately 5,730 years). The rest of the carbon is not radioactive. As a result, about one trillionth of the carbon in the tissues of a living plant or animal is that radioactive form of carbon. This ratio of carbon-14 to nonradioactive carbon in the air and living tissue has remained fairly constant6because the rate at which carbon-14 is created (through an interaction of cosmic radiation with the nitrogen in the upper atmosphere) matches the rate at which it decays.At death, however, the plant or animal stops absorbing carbon, and the tiny amount of carbon-14 in its tissues begins to decrease due to radioactive decay. By measuring the current ratio of carbon-14 to the nonradioactive carbon in a tissue sample (say, a piece of old bone or wood), and then comparing this ratio to theratio in comparable living tissue, a good estimate of the fraction of the carbon-14 that has decayed can be made. Using that and our model for radioactive decay, the age of the bone or wood can then be approximated.
Hydrochemistry and groundwater isotopes
Published in Ian Acworth, Investigating Groundwater, 2019
Carbon has two stable, non-radioactive isotopes: carbon-12 (12C) and carbon-13 (13C). In addition there are trace quantities of the unstable isotope carbon-14 (14C) on the earth’s surface. Carbon-14 has a half-life of only 5730 years if it did not get constantly replenished in the upper atmosphere. The means of renewal is the impact of cosmic rays from the sun reacting on nitrogen in the upper atmosphere of the earth via the reaction: n+714N→614C+p
Soil-Water Budget
Published in Daniel B. Stephens, Andrea J. Kron, Andrea Kron, Vadose Zone Hydrology, 2018
Daniel B. Stephens, Andrea J. Kron, Andrea Kron
Carbon-14 is a radioactive isotope of carbon produced in the upper atmosphere by cosmic ray interactions with nitrogen. The carbon becomes part of the carbon dioxide molecule that dissolves in the water, enters the soil gas, and becomes part of the animal or plant tissue. When the water or soil gas no longer is free to exchange with the atmosphere, and when the animal or plant dies, the carbon-14 activity decreases at a rate controlled by its half-life, 5730 years. The concentration or activity ratio of carbon-14 to carbon-12, expressed as a percent, is called the percent modern carbon, pmc. Except for input from thermonuclear testing in the 1950s and 1960s, this ratio has remained relatively constant, varying only by a factor of about two, in the atmosphere over the last 100,000 years (Phillips, 1995). Inasmuch as carbon-14 is detectable to about 1 pmc, the potential usefulness of the age dating method is about 40,000 years (Mazor, 1991), based on Equation 23, but in most groundwater investigations the practical limit is about half this (Phillips, 1995).
Searching for optimal accident tolerant fuel for the VVER-1200 reactor from the neutronic point of view
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2023
A. Abdelghafar Galahom, Ehab M. Aboelyazid, S.A. EL-Fiki, Moustafa Aziz
The radioactive carbon (14C) half-life is 5730 years. The main drawback of the 14C is its high mobility in the environment. It can diffuse into the environment in the form of gaseous and liquid discharges and the disposal of radioactive waste. When 14C decays, a low-energy beta particle is released; if this radiation is discharged within the body, it might cause cell damage. Consequently, it is crucial to study the 14C mass with burnup. Figure 17 displays the 14C mass with burnup. The 14C is formed in the reactor when a neutron collides with a nitrogen atom (14N). Therefore, the 14C mass increases linearly with burnup in the case of U14N.