Carbon-14 is a radioactive isotope and is present in all living things in a constant amount.
Because of the carbon cycle, there is always carbon-14 present in both the air and in living organisms.
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For the record, a beta-particle is a specific type of nuclear decay. Image 1 shows carbon-14 production by high energy neutrons hitting nitrogen-14 atoms, while in Image 2, carbon-14 naturally decomposes through beta-particle production.
Notice that the nitrogen-14 atom is recreated and goes back into the cycle.
You might remember that it was mentioned earlier that the amount of carbon-14 in living things is the same as the atmosphere.