Radiometric dating practice questions

But there are some questions that come to mind: Calculus students typically meet this problem somewhere in the second semester.It is one of the simplest examples of a differential equation.Imagine we have an undiscovered element, Parentium, that has a radioactive isotope, Parentium-123, which decays to stable Daughterium-123.This is the only way Parentium-123 decays, and there is no other source of Daughterium-123.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 time it takes for half of a sample to decay is called a “half-life.” By measuring radioactive half-lives, by measuring how much parent and daughter are present in any given specimen, and by making certain key assumptions, scientists believe they are able to accurately determine the age of a specimen. The question is what are the underlying key assumptions and how reliable are they?

It's just a little section of the surface of the Earth. And that carbon-14 that you did have at you're death is going to decay via beta decay-- and we learned about this-- back into nitrogen-14. So it'll decay back into nitrogen-14, and in beta decay you emit an electron and an electron anti-neutrino. But essentially what you have happening here is you have one of the neutrons is turning into a proton and emitting this stuff in the process. So I just said while you're living you have kind of straight-up carbon-14. What it's essentially saying is any given carbon-14 atom has a 50% chance of decaying into nitrogen-14 in 5,730 years.

And it has seven protons, and it also has seven neutrons. So the different versions of a given element, those are each called isotopes. So anyway, we have our atmosphere, and then coming from our sun, we have what's commonly called cosmic rays, but they're actually not rays. You can view them as just single protons, which is the same thing as a hydrogen nucleus. But every now and then one of those neutrons will bump into one of the nitrogen-14's in just the right way so that it bumps off one of the protons in the nitrogen and essentially replaces that proton with itself. But this number 14 doesn't go down to 13 because it replaces it with itself. And now since it only has six protons, this is no longer nitrogen, by definition. And that proton that was bumped off just kind of gets emitted. But this process-- and once again, it's not a typical process, but it happens every now and then-- this is how carbon-14 forms. You can essentially view it as a nitrogen-14 where one of the protons is replaced with a neutron. It makes its way into oceans-- it's already in the air, but it completely mixes through the whole atmosphere-- and the air. And plants are really just made out of that fixed carbon, that carbon that was taken in gaseous form and put into, I guess you could say, into kind of a solid form, put it into a living form. It gets put into plants, and then it gets put into the things that eat the plants. Well, the interesting thing is the only time you can take in this carbon-14 is while you're alive, while you're eating new things.

When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.

Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.

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