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I came across a PreCalc decay problem dealing with trying to date an old piece of wood found at a archaeological dig. The half-life of carbon-14 was given as 5600 years.

The problem was: 2% of the original carbon amount remains. When was the tree cut down?

My question is: How do they know the original amount of carbon-14 in the wood? Did someone plant a new tree of the same type and measure the initial amount of carbon-14?

Also, is the amount of carbon-14 uniform across all samples of this wood? Does it start and decay exactly the same for all samples of this type of wood? What if it's just a particularly high concentration in this piece of wood b/c of was facing the sun (or whatever) Would you take several samples from the wood?

Also, does this belong in some Science subforum?

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This belongs in another forum. –  copper.hat Feb 5 '13 at 19:22
    
The tinier the sample, the more variation there is. More samples is always better. If sample is very old, little Carbon $14$ is left, so measurements are unreliable. There is some variation caused by conditions, not a large amount. There have also been variations in the relative amount of Carbon $14$ in the atmosphere. A huge amount of work has been done to refine the basic idea used in textbook examples. –  André Nicolas Feb 5 '13 at 19:34

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There are many potential errors in carbon-14 dating, some of which you have identified. We know the current percentage of C-14 in the atmosphere. It is produced by cosmic rays and should be evenly distributed by wind. Since (almost all) the carbon in a plant comes from the atmosphere, we assume that the carbon in the plant is that percentage C-14. During life, the carbon is replaced, so the percentage should stay about the same, and the half-life of C-14 is long compared to plant lifetimes, so this shouldn't be bad. It is known that organic reactions favor the lighter isotopes, more so when the temperature is low, so the percentage in the tree during life is lower that the atmosphere. Then when the tree dies, the carbon is no longer replaced and decays.

But you can do the calculation on this basis and be fairly close.

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