Anything that dies after the 1940s, when Nuclear bombs, nuclear reactors and open-air nuclear tests started changing things, will be harder to date precisely.
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At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.
When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.
At the present time, for a 1 milligram sample of graphite, this limiting age is about ten half-lives, or 60,000 years, if set only by the sample size.
However, limiting ages or "backgrounds" are also determined by process blanks which correspond to the method used to extract the carbon from the sample.
This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50,000 years ago.