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.
If this water is in contact with significant quantities of limestone, it will contain many carbon atoms from dissolved limestone.
Since limestone contains very little, if any, radiocarbon, clam shells will contain less radiocarbon than would have been the case if they had gotten their carbon atoms from the air.
First, any instrument which is built to measure radiocarbon has a limit beyond which it cannot separate the signal due to radiocarbon in the sample from the signal due to background processes within the measuring apparatus.
Even a hypothetical sample containing absolutely no radiocarbon will register counts in a radiocarbon counter because of background signals within the counter.
Thus, it is possible (and, given the Flood, probable) that materials which give radiocarbon dates of tens of thousands of radiocarbon years could have true ages of many fewer calendar years. The shells of live freshwater clams have been radiocarbon dated in excess of 1600 years old, clearly showing that the radiocarbon dating technique is not valid.
It is not difficult to see how such a claim could arise, however.
There are two characteristics of the instrumental measurement of radiocarbon which, if the lay observer is unaware, could easily lead to such an idea.
Long tree-ring chronologies are rare (there are only two that I am aware of which are of sufficient length to be of interest to radiocarbon) and difficult to construct.
They have been slowly built up by matching ring patterns between trees of different ages, both living and dead, from a given locality.