Carbon dating calculus
Radiocarbon dating uses isotopes of the element carbon. Cosmic rays – high energy particles from beyond the solar system – bombard Earth’s upper atmosphere continually, in the process creating the unstable carbon-14. Because it’s unstable, carbon-14 will eventually decay back to carbon-12 isotopes.
Because the cosmic ray bombardment is fairly constant, there’s a near-constant level of carbon-14 to carbon-12 ratio in Earth’s atmosphere.
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This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50,000 years ago.
SAL: In the last video we saw all sorts of different types of isotopes of atoms experiencing radioactive decay and turning into other atoms or releasing different types of particles.
But the question is, when does an atom or nucleus decide to decay? So it could either be beta decay, which would release electrons from the neutrons and turn them into protons. And normally when we have any small amount of any element, we really have huge amounts of atoms of that element. That's 6.02 times 10 to the 23rd carbon-12 atoms. This is more than we can, than my head can really grasp around how large of a number this is.
Exactly the same treatment can be applied to radioactive decay.
However, now the "thin slice" is an interval of time, and the dependent variable is the number of radioactive atoms present, N(t). If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval.