system
Given the following post, respond as if you're commenting on Reddit:
human
How did scientist come up with and prove carbon dating?
gpt
So, as you may know, the number of protons in an atom determines what kind of element it is. In it's stable form, carbon has 6 protons and 6 neutrons, and is otherwise known as carbon 12. Nitrogen, the next element on the periodic table, is most stable with 7 protons and 7 neutrons, aka nitrogen 14. 

Sunlight in our atmosphere causes atomic particles, like neutrons, to be blasted around (I can explain this more if you'd like). When normal Nitrogen 14 in the atmosphere comes into contact with a free flying neutron, it causes that nitrogen atom to gain the neutron, but also to immediately lose a proton. Since the atom now has 6 protons, it is officially carbon, but since it also has 8 neutrons, it is an unstable (and radioactive) form of carbon, Carbon 14. Carbon 14 behaves just like regular carbon, but since it is radioactive, it slowly decays into stable Carbon 13. This decay can be detected using a Geiger counter and its relative abundance can be quite easily measured.

Carbon 14 is generated in the atmosphere at a very constant rate, making it's concentration both in the air and inside every LIVING thing quite predictable (about 1 per trillion carbon atoms). However, when organisms die, they stop recycling carbon, so they no longer collect new Carbon 14. The Carbon 14 that they do have slowly decays, so the organism's concentration of the radioactive isotope is also slowly depleted.

Depending on when an organism lived (whether it's a tree 50,000 years ago or a squirrel 30 years ago) it will have some amount of Carbon 14 remaining. As such, the ratio of carbon 14 to stable carbon atoms can give us a very accurate measure of how long ago this organism stopped taking in new carbon (died). This is the basis of carbon dating.

TL;DR - carbon 14, a radioactive isotope of carbon, is generated at a constant rate in our atmosphere. Its concentration in the atmosphere is mirrored in all living organisms. When an organism dies, it's concentration of c14 slowly depletes. Depending on the ratio of remaining radioactive carbon to stable carbon, we can quite accurately estimate how long ago the organism lived.