We can't date oil paints, because their oil is "old" carbon from petroleum. And third, it is common to soak new-found fossils in a preservative, such as shellac.
It is also standard to coat fossils during their extraction and transport.
The approach was a sensation when it was introduced.
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For radiocarbon dating to be possible, the material must once have been part of a living organism.
This means that things like stone, metal and pottery cannot usually be directly dated by this means unless there is some organic material embedded or left as a residue.
All animals in the food chain, including carnivores, get their carbon indirectly from plant material, even if it is by eating animals which themselves eat plants.
The net effect of this is that all living organisms have the same radiocarbon to stable carbon ratio as the atmosphere.
Common materials for radiocarbon dating are: The radiocarbon formed in the upper atmosphere is mostly in the form of carbon dioxide. Because the carbon present in a plant comes from the atmosphere in this way, the radio of radiocarbon to stable carbon in the plant is virtually the same as that in the atmosphere.
Plant eating animals (herbivores and omnivores) get their carbon by eating plants.
Obviously there will usually be a loss of stable carbon too but the proportion of radiocarbon to stable carbon will reduce according to the exponential decay law: R = A exp(-T/8033) where R is C ratio of the living organism and T is the amount of time that has passed since the death of the organism.
By measuring the ratio, R, in a sample we can then calculate the age of the sample: T = -8033 ln(R/A) Both of these complications are dealt with by calibration of the radiocarbon dates against material of known age.
This leaves out aquatic creatures, since their carbon might (for example) come from dissolved carbonate rock.
That causes a dating problem with any animal that eats seafood. After about ten half-lives, there's very little C14 left.
The dating process is always designed to try to extract the carbon from a sample which is most representative of the original organism.