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.
In the following article, some of the most common misunderstandings regarding radiocarbon dating are addressed, and corrective, up-to-date scientific creationist thought is provided where appropriate. Radiocarbon is used to date the age of rocks, which enables scientists to date the age of the earth.
There are two characteristics of the instrumental measurement of radiocarbon which, if the lay observer is unaware, could easily lead to such an idea.
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).
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.