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Mass spectroscopy, like any man-made measurement, is not perfect. It doesn't take much contamination to spoil a sample with near-zero quantity of C14. Nearby radioactive material could trigger exactly the same C14 production process from nitrogen as occurs in the upper atmosphere, albeit at a much reduced rate.
In particular, given a pure sample of C12, I suspect a mass spectrometer would indicate that a non-zero amount of C14 present. Creationists pounce on this explanation as meaning all carbon 14 readings are suspect. While that same level of contamination (if this is the explanation) will add some error to the dating of some reasonably aged sample, the error will be small -- so long as the sample is not too old. Another possible avenue is C13, which has a small but non-zero neutron absorption cross section.
A standard test for determining if ethanol is made from plants (making it legal for human consumption) or petroleum (making it illegal) is to measure the C14.
In fact, if every atom making up the earth was carbon-14, even after just 1 million years there would be absolutely no atoms of carbon-14 left, because they would have all decayed away, based on today’s measured half-life!
That’s why radiocarbon dating isn’t used to date rocks at millions of years.
The RATE radiocarbon research first focused on demonstrating that significant detectable levels of carbon-14 are present in ancient coal beds.12 Ten samples from U. coal beds, conventionally dated at 40–320 million years old, were found to contain carbon-14 equivalent to ages of around 48,000–50,000 years.
The laboratory did repeat analyses and confirmed that this carbon-14 in the coals was not due to any contamination either in situ in the samples or added to the samples in the laboratory.