EXAMPLE 6 Carbon-14 Dating

How much of the original carbon-14 would be left after 50,000 years? (This is roughly the practical age limit for carbon-14 dating of the typically small samples available.) How many atoms would be decaying per hour per gram of carbon?

We have

so only about 0.24% of the original amount remains. This remaining amount would be decaying at a rate of atoms per hour per gram of carbon. An accurate estimate for the age of a sample of 1 milligram (mg) of carbon might take weeks or months of tallying counts on a decay counter. (The analysis is now often done by much faster atomic mass spectrometry rather than by counting decays, and calibration adjustments must be made for varying amounts of atmospheric carbon-14 over the years. Our calculations do not take such calibration, much of which is done from tree rings, into account.)