If you've been reading the sections of this Hot Science in order, you already
know that, to determine the age of an object through radiocarbon dating, you
need to know the amount of carbon-14 that the once-living organic specimen
started off with as well as the rate that carbon-14 decays, both of which we do
know.

All that's left to determine is the ratio between carbon-12 atoms and carbon-14
atoms within the specimen to be dated. How is this done?

One way is to use a particle accelerator. Here's how the method works:

All of the carbon atoms from a small sample of the specimen are fed through the
accelerator. The speeding atoms then pass through a magnetic field.

The magnetic field deflects all the atoms, but to varying degrees. A detector—one that can count any type of carbon atom—is situated in a position that
only the carbon-14 atoms reach. The detector, therefore, counts only the
carbon-14 atoms within the sample.

With the total number of carbon-14 atoms counted and the knowledge of the total
number of carbon atoms, one can determine the ratio of carbon-12 to carbon-14. How
far off this ratio is from the initial carbon-12 to carbon-14 ratio (which is,
by the way, about one trillion to one), reveals how much of the carbon-14 has
decayed. Then all that's left to be done is to figure out, based on carbon-14's
half-life of 5,730 years, how much time has elapsed.

Actually, it's a little more complicated than that. The radiocarbon date
doesn't match up exactly with actual years elapsed. One reason is that the
amount of carbon-14 in the atmosphere has not always been constant. But one can
make adjustments to the date, and if the age of the item is 40,000 years old or
younger, one can arrive at a relatively accurate figure.