Radiometric dating methods detect beta particles from the decay of carbon 14 atoms while accelerator mass spectrometers count the number of carbon 14 atoms present in the sample.
Both carbon dating methods have advantages and disadvantages.
These two radiocarbon dating methods use modern standards such as oxalic acid and other reference materials.
Although both radiocarbon dating methods produce high-quality results, they are fundamentally different in principle.
We note that at the instant the swimmer touches the end of the pool our wristwatch reads and 53 seconds.
How long has the competitor taken to swim the race?
And you have to check to make sure he touches the end for each lap.
Without these observations you cannot be sure that the time is valid.
During the race you have to watch the swimmer and count how many laps he has swum so you know that he has done 1,500 metres.
Thanks to nuclear physics, mass spectrometers have been fine-tuned to separate a rare isotope from an abundant neighboring mass, and accelerator mass spectrometry was born.
A method has finally been developed to detect carbon 14 in a given sample and ignore the more abundant isotopes that swamp the carbon 14 signal.
The educational page hosted by the US Geological Society provides one recent example of the way radioactive dating is explained to the public.
They focus on the technicalities of radioactive decay, etc.