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(2) A half-life is the time needed for half the initial number of radioactive nuclei to disintegrate.
Therefore, other methods such as OSL (Optically Stimulated Luminescence dating) or isotopes with longer half-lives researchers studying US bristle cone pine and German and Irish oaks discovered fluctuations in the C14 concentration.
Measurements of the Libby half-life showed that Libby was about .3% too low.
A fluorescence event is proportional to the decay event of C14; and the frequency is proportional to the number of C14 atoms in the sample.
Instead of measuring the radioactivity of the sample (as in LCS); Accelerator Mass Spectrometry (AMS) counts directly the radiocarbon atoms.
An age could be estimated by measuring the amount of carbon-14 present in the sample and comparing this against an internationally used reference standard.