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This process is constantly occurring, and has been for a very long time, so there is a fairly constant ratio of carbon 14 atoms to carbon 12 atoms in the atmosphere. Now living plants 'breathe' CO 2 indiscriminately they don't care about isotopes one way or the other , and so while they are living they have the same ratio of carbon 14 in them as the atmosphere.
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Animals, including humans, consume plants a lot and animals that consume plants , and thus they also tend to have the same ratio of carbon 14 to carbon 12 atoms. This equilibrium persists in living organisms as long as they continue living, but when they die, they no longer 'breathe' or eat new 14 carbon isotopes Now it's fairly simple to determine how many total carbon atoms should be in a sample given its weight and chemical makeup.
And given the fact that the ratio of carbon 14 to carbon 12 in living organisms is approximately 1: In actually measuring these quantities, we take advantage of the fact that the rate of decay how many radioactive emissions occur per unit time is dependent on how many atoms there are in a sample this criteria leads to an exponential decay rate. We have devices to measure the radioactivity of a sample, and the ratio described above translates into a rate of Voila, now you can tell how old a sample of organic matter is. Carbon 14 dating is not great for dating things like a year old because if much less than 1 half-life has passed, barely any of the carbon 14 has decayed, and it is difficult to measure the difference in rates and know with certainty the time involved.
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