It's not that the radioactive carbon in air or food doesn't decay, it does.
Everything from the fibres in the Shroud of Turin to Otzi the Iceman has had their birthday determined the carbon-14 way. There's plenty of hydrogen, oxygen and nitrogen in living things too, but carbon's got something none of them do — a radioactive isotope that can take thousands of years to decay.
(You can read up on radioactivity and isotopes here).
Carbon-14, the radioactive version of carbon, is rare — it only makes up one trillionth of all the carbon in the world.
And that something else starts where Earth meets space.
Earth's upper atmosphere is constantly being bombarded by cosmic rays (usually protons travelling at nearly the speed of light).
Not only that, we top up our carbon-14 levels every time we eat.And plants top up their radioactive carbon every time they turn carbon dioxide to food during photosynthesis.For a rare event it happens pretty damn often — one million carbon-14 atoms in your body decay into nitrogen every minute!But don't panic — of the 800,000,000,000,000,000,000,000,000 carbon atoms in every one of us, about 800,000,000,000,000 are carbon-14, so we've got a few to spare.Chemically, carbon-14 is no different from non-radioactive carbon atoms, so it ends up in all the usual carbon places — one trillionth of the carbon atoms in air, plants, animals and us are radioactive.All radioactive atoms eventually decay into something more stable, and carbon-14 decays into nitrogen.