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Carbon-14 cannot be used to date biological artifacts of organisms that did not get their carbon dioxide from the air.

This rules out carbon dating for most aquatic organisms, because they often obtain at least some of their carbon from dissolved carbonate rock.

Levels of carbon-14 become difficult to measure and compare after about 50,000 years (between 8 and 9 half lives; where 1% of the original carbon-14 would remain undecayed).

The question should be whether or not carbon-14 can be used to date any artifacts at all? There are a few categories of artifacts that can be dated using carbon-14; however, they cannot be more 50,000 years old.

The meaning of this equation is that the rate of change of the number of nuclei over time is proportional only to the number of nuclei.

Example: A young-Earth research group reported that they sent a rock erupted in 1980 from Mount Saint Helens volcano to a dating lab and got back a potassium-argon age of several million years.

This shows we should not trust radiometric dating, right? The potassium-argon method, with its long half-life of 1.3 billion years, should not be used to date rocks that are only 25 years old.

Some isotopes have half lives longer than the present age of the universe, but they are still subject to the same laws of quantum physics and will eventually decay, even if doing so at a time when all remaining atoms in the universe are separated by astronomical distances.

Various elements are used for dating different time periods; ones with relatively short half-lives like carbon-14 (or C) are useful for dating once-living objects (since they include atmospheric carbon from when they were alive) from about ten to fifty thousand years old. Longer-lived isotopes provide dating information for much older times.