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In the early days of radiocarbon analysis this limit was often around 20,000 radiocarbon years.
Thus, all the researcher was able to say about samples with low levels of radiocarbon was that their age was greater than or equal to 20,000 radiocarbon years (or whatever the sensitivity limit of his apparatus was).
It is not correct to state or imply from this evidence that the radiocarbon dating technique is thus shown to be generally invalid.
The problem with freshwater clams arises because these organisms derive the carbon atoms which they use to build their shells from the water in their environment.
For example, a sample with a true radiocarbon age of 100,000 radiocarbon years will yield a measured radiocarbon age of about 20,000 radiocarbon years if the sample is contaminated with a weight of modern carbon of just 5% of the weight of the sample's carbon.
It is not too difficult to supply contaminating radiocarbon since it is present in relatively high concentrations in the air and in the tissues of all living things including any individuals handling the sample.
Reports of young radiocarbon ages for coal probably all stem from a misunderstanding of one or both of these two factors.
The shells of live freshwater clams can, and often do, give anomalous radiocarbon results.
However, the reason for this is understood and the problem is restricted to only a few special cases, of which freshwater clams are the best-known example.
I am not aware of any authentic research which supports this claim.
Also, it does not coincide with what creationist scientists would currently anticipate based upon our understanding of the impact of the Flood on radiocarbon.