Radiometric dating calculus equations
Furthermore, Parentium and Daughterium are so different in chemical properties that they don't otherwise occur together.If there were such a pair of isotopes, radiometric dating would be very simple.
Since there is now only 1/4 of the original amount of Parentium-123, we know that two half-lives of Parentium-123 have elapsed.What I want to do in this video is kind of introduce you to the idea of, one, how carbon-14 comes about, and how it gets into all living things. They can also be alpha particles, which is the same thing as a helium nucleus. And they're going to come in, and they're going to bump into things in our atmosphere, and they're actually going to form neutrons. And we'll show a neutron with a lowercase n, and a 1 for its mass number. And what's interesting about this is this is constantly being formed in our atmosphere, not in huge quantities, but in reasonable quantities. Because as soon as you die and you get buried under the ground, there's no way for the carbon-14 to become part of your tissue anymore because you're not eating anything with new carbon-14.And then either later in this video or in future videos we'll talk about how it's actually used to date things, how we use it actually figure out that that bone is 12,000 years old, or that person died 18,000 years ago, whatever it might be. So let me just draw the surface of the Earth like that. So then you have the Earth's atmosphere right over here. And 78%, the most abundant element in our atmosphere is nitrogen. And we don't write anything, because it has no protons down here. And what's interesting here is once you die, you're not going to get any new carbon-14. You can't just say all the carbon-14's on the left are going to decay and all the carbon-14's on the right aren't going to decay in that 5,730 years.The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000).And it'll get a little bit mathy, usually involving a little bit of algebra or a little bit of exponential decay, but to really show you how you can actually figure out the age of some volcanic rock using this technique, using a little bit of mathematics.
So we know that anything that is experiencing radioactive decay, it's experiencing exponential decay.
And we talk about the word isotope in the chemistry playlist. But this number up here can change depending on the number of neutrons you have. And every now and then-- and let's just be clear-- this isn't like a typical reaction. So instead of seven protons we now have six protons. And a proton that's just flying around, you could call that hydrogen 1. If it doesn't gain an electron, it's just a hydrogen ion, a positive ion, either way, or a hydrogen nucleus. And so this carbon-14, it's constantly being formed. I've just explained a mechanism where some of our body, even though carbon-12 is the most common isotope, some of our body, while we're living, gets made up of this carbon-14 thing.
So carbon by definition has six protons, but the typical isotope, the most common isotope of carbon is carbon-12. And then that carbon dioxide gets absorbed into the rest of the atmosphere, into our oceans. When people talk about carbon fixation, they're really talking about using mainly light energy from the sun to take gaseous carbon and turn it into actual kind of organic tissue.
But we know that the amount as a function of time-- so if we say N is the amount of a radioactive sample we have at some time-- we know that's equal to the initial amount we have.
We'll call that N sub 0, times e to the negative kt-- where this constant is particular to that thing's half-life.
But there are some questions that come to mind: Calculus students typically meet this problem somewhere in the second semester.