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The reason is that, as long as the organism is alive, it replaces any carbon molecule that has decayed into nitrogen.
After plants and animals perish, however, they no longer replace molecules damaged by radiocarbon decay.
Many people assume that rocks are dated at “millions of years” based on radiocarbon (carbon-14) dating. The most well-known of all the radiometric dating methods is radiocarbon dating.
Carbon-14 can yield dates of only “thousands of years” before it all breaks down.
After radiocarbon forms, the nuclei of the carbon-14 atoms are unstable, so over time they progressively decay back to nuclei of stable nitrogen-14.3 A neutron breaks down to a proton and an electron, and the electron is ejected. The ejected electrons are called beta particles and make up what is called beta radiation. Different carbon-14 atoms revert to nitrogen-14 at different times, which explains why radiocarbon decay is considered a random process.
To measure the rate of decay, a suitable detector records the number of beta particles ejected from a measured quantity of carbon over a period of time, say a month (for illustration purposes).
If we know what fraction of the carbon atoms are radioactive, we can also calculate how many radiocarbon atoms are in the lump.
If we assume that the mammoth originally had the same number of carbon- 14 atoms in its bones as living animals do today (estimated at one carbon-14 atom for every trillion carbon-12 atoms), then, because we also know the radiocarbon decay rate, we can calculate how long ago the mammoth died. This dating method is similar to the principle behind an hourglass.6 The sand grains that originally filled the top bowl represent the carbon-14 atoms in the living mammoth just before it died.
Radioactive and non-radioactive carbon dioxide mix throughout the atmosphere, and dissolve into the oceans.
Through photosynthesis carbon dioxide enters plants and algae, bringing radiocarbon into the food chain.
It’s assumed to be the same number of carbon-14 atoms as in elephants living today.
With time those sand grains fall to the bottom bowl, so the new number represents the carbon-14 atoms left in the mammoth skull when we found it.
Since each beta particle represents one decayed carbon-14 atom, we know how many carbon-14 atoms decay during a month.