How does carbon dating work?
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Almost all carbon in the atmosphere is carbon-12. This is what you would think of as “normal” stable carbon. However, there is _some_ carbon that is carbon-14 – a radioactive isotope of carbon that has a half-life of 5,730 years. This means that after 5,730 years, half of the carbon-14 in something will decay into nitrogen-14.
When something is alive, it will have an expected ratio of carbon-12 to carbon-14 (based on normal concentrations for that time period). However, once that thing dies, the carbon inside the thing is “fixed.” We can use that fact to look at the ratios of carbon-12 to 14 to determine how much of the carbon-14 has decayed, which will tell us how long ago the thing died.
It only works for things that are less than ~50k years old; after that point, too much of the carbon-14 has decayed and we have to use other dating methods.
We track one of the carbon isotopes, one that’s very rare and radioactive, called radiocarbon. This radiocarbon, being radioactive, decays over time, reducing in amount (and turning into regular carbon). Since it’s mostly a constant amount being produced, by measuring how much radiocarbon there is, you can tell how long it has been decaying. If you know how long it has been decaying, you know when it died.
There are two types of Carbon: C12 and C14. C14 is unstable and will eventually decay into C12.
C14 is constantly being produced from C12 in the higher levels of the atmosphere through interactions with cosmic rays. The rate that C14 is being generated (by these interactions) and being lost (through radioactive decay) is essentially the same, meaning the amount of C14 stays roughly constant.
Your body has carbon in it and that carbon came from the carbon in the atmosphere. This means that your body has the same ratio of C12:C14 as the atmosphere and this ratio is maintained because your body keeps replenishing itself.
When you die, your body stops replenishing itself and the carbon in your body when you die is no longer getting updated. That means the C14 in your body gradually decays into C12 but is never refreshed from the atmosphere because you’re dead.
Since we know the ratio of C12:C14 that was in your body while alive, and since we know the decay rate of C14 into C12, we can measure the ratio of C12:C14 in your dead body now and figure out how long it has been dead.
radiation from space makes some carbon in the atmosphere radioactive. you breathe it in and it becomes part of your body. when you stop breathing in more of it, eventually all the radioactive carbon in your body runs out and stops being radioactive. this takes a very long time and scientists can tell when you stopped breathing because of how much radioactive carbon is left.
the space radiation is the important part; that’s why there’s more radioactive carbon floating around than there is in dead things. carbon dating is measuring how long something has been cut off from the source of radioactive carbon.
Any radioactive isotope has a half life (5730 years in carbin 14). For a given quantity of that isotope, after one half life, half of that isotope would have decayed into its children. In the case of carbon 14, it would have beta decayed, resulting in nitrogen 14 (normal nitrogen) and an electron. We know how much carbon 14 there is in relation to carbon 12 (normal carbon) here on Earth, and any sample of (non isolated) carbon you take randomly should contain that same ratio of carbon 12 to carbon 14.
All living things ingest carbon in some form, so naturally something that’s constantly ingesting carbon from the environment, should have the same ratio of carbon 12 to carbon 14 in their bodies as that environment. Once that organism dies, it stops taking in carbon, so that carbon is now isolated. After 5730 years, half of the carbon 14 in that organism has decayed, so the ratio of carbon 12 to carbon 14 should be different, showing half as much carbon 14 as in the environment, so we know that the organism died 5730 years ago. Different ratios allow us to find different amounts of time, but after about 10 half lives or so, the ratio becomes too hard to measure, but then you can often use something of a longer half life like uranium.
The same can also be applied to say pottery. The clay out in the environment constantly has things dying in it, introducing carbon, until a human takes the clay out of the environment and fires it, isolating that carbon and allowing us to figure out when it was made.
Half lives are also not a fundamental law of how radioactivity works, but rather a result of statistics. A radioactive atom, after one half life, has a 50% of decaying. It isn’t communicating with all of its neighbors to work out which atoms decay when, there’s just so many atoms that after one half life, half of them have decayed, but if it’s off by a couple hundred atoms, no one will notice among the billions of atoms in the sample you’re taking. The sample size is so large, that we can always assume it behaves that way.
The formula:
Remaining isotope = initial isotope * e^(-[ln2/half life] * time)
Carbon consists of C-14 and C-12 isotypes, with it being almost entirely c-12.
C-14 acts chemically the same as C-12. But it is slightly radioactive.
We know roughly how many % C-14 there is/was in the atmosphere at different times.
When you are alive and exchanging carbon the % of C-14 will be basically the same as in the atmosphere, however once you die you are stuck with that carbon. And since C-14 is slightly radioactive the amount slowly decreases over time.
So you measure the % of C-14 compared to what is expected and make deductions from that.
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