Hi Jabba,
I think the problem with your calculation is that it assumes the loss of C14 is linear over time. The loss of C14 is exponential since the loss of C14 is proportional to the amount of C14 at any one time. That is when there is less C14 less C14 is lost. The effect of this is to make it so that the rate at which C14 is lost declines with time.
When I did my calculation I just used the data supplied by Aepervius which was:
Modern carbon 100% 1 carbon 14C per 1 trillion C so 6.0 10^11 per mole
0 AD carbon 78% 0,78 carbon 14C per 1 trillion C so ~4,7 10^11 per mole
Seemingly 1250 AD 91% 0,91 carbon 14C per 1 trillion C so ~5,5 10^11 per mole
I didn't check him on the data but my guess is that he got it from a chart that showed C14 concentrations with date. Initially when C14 testing was done people assumed that C14 concentrations with time could be calculated by assuming an exponential decline. It turned out that when methods for calibrating C14 testing were developed that the initial assumptions were wrong. The amount of C14 in the atmosphere does vary a bit with time so it is necessary to correct estimates of C14 concentrations with time based on calibration testing. As an aside, one of my favorite places is the White Mountains in California where bristlecone pines grow. Bristlecone pines were the first source of data that was used to calibrate C14 testing. Some of the living bristlecone pines are 5000 years old and these could be dated precisely by tree ring analysis. But they were even able to push that back farther because the White Mountains are so dry that there are very old dead trees that had rings that overlapped in time with living trees. Using the old trees they were able to provide a calibration scale for C14 testing that went back about 10,000 years.
I am afraid that I might not have explained exponential decay very well. You might look at the Wikipedia article and see if that doesn't make sense:
http://en.wikipedia.org/wiki/Exponential_growth
As an another aside, Aepervius calculated 1.44 for the amount of contaminating material to original source material required. He and I communicated outside this thread and his number is a bit more accurate than my answer which was 1.6. There was a rounding error in my calculation. When I used the C14 concentrations rounded to two places rather than one I also got the same answer. I tried to find a calculation by an expert on line and didn't find one to provide further verification that we had done the calculation correctly. I did find an expert that said the amount of contamination required was almost double so our answer is in the ball park with that.
Regardless, I think you can see that whether the answer is .96, 1.6 or 1.44 a very large amount of contamination would be required and eliminating contamination by careful cleaning seems to be part of all C14 testing. I have seen two contamination theories: Bioplastic and soot. The expert I read rejected the notion of bioplastic contamination entirely. I think the idea on the bioplastic contamination was that somehow a lot of touching had created a kind of film on the sampled area. There doesn't seem to be any evidence for something like that and as you can see it would take a whole lot of bioplastic contamination to skew the result by 1300 years or so. The idea of soot contamination seems even more remote. Even given that soot is nearly pure carbon it would still take a lot of soot to skew the result and soot is very visible. I think people would have noticed even a tiny fraction of the amount of soot required to skew the result in the sample.
