Write the nuclide symbol for carbon 13 dating

Explainer: what is radiocarbon dating and how does it work?

Carbon nuclear medicine: Another isotope, carbon, is useful in studying Carbon, which is radioactive, is the isotope used in radiocarbon dating and atmosphere collide with neutrons produced by the interaction of high-energy. Atoms of the same element that have different numbers of neutrons are called isotopes. as the very stable isotope carbon, with a very small amount as carbon In The Cosmic Story of Carbon Ethan Siegel writes. Carbon is the common isotope, with carbon as another stable isotope which makes up about 1%. Carbon 14 is radioactive and the basis for carbon dating.

So let me write this down. And let me be very clear. Let's look at the periodic table over here. So carbon by definition has six protons, but the typical isotope, the most common isotope of carbon is carbon So carbon is the most common.

So most of the carbon in your body is carbon But what's interesting is that a small fraction of carbon forms, and then this carbon can then also combine with oxygen to form carbon dioxide.

How Does Carbon Dating Work

And then that carbon dioxide gets absorbed into the rest of the atmosphere, into our oceans. It can be fixed by plants. 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. And so this carbon, it's constantly being formed. It makes its way into oceans-- it's already in the air, but it completely mixes through the whole atmosphere-- and the air.

And then it makes its way into plants. 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. That's what wood pretty much is. It gets put into plants, and then it gets put into the things that eat the plants. So that could be us. Now why is this even interesting? I've just explained a mechanism where some of our body, even though carbon is the most common isotope, some of our body, while we're living, gets made up of this carbon thing.

Well, the interesting thing is the only time you can take in this carbon is while you're alive, while you're eating new things. Because as soon as you die and you get buried under the ground, there's no way for the carbon to become part of your tissue anymore because you're not eating anything with new carbon And what's interesting here is once you die, you're not going to get any new carbon And that carbon that you did have at you're death is going to decay via beta decay-- and we learned about this-- back into nitrogen So kind of this process reverses.

So it'll decay back into nitrogen, and in beta decay you emit an electron and an electron anti-neutrino. I won't go into the details of that. 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. Now why is this interesting? So I just said while you're living you have kind of straight-up carbon And carbon is constantly doing this decay thing.

But what's interesting is as soon as you die and you're not ingesting anymore plants, or breathing from the atmosphere if you are a plant, or fixing from the atmosphere.

Carbon 14 dating 1 (video) | Khan Academy

And this even applies to plants. Once a plant dies, it's no longer taking in carbon dioxide from the atmosphere and turning it into new tissue.

write the nuclide symbol for carbon 13 dating

The carbon in that tissue gets frozen. And this carbon does this decay at a specific rate. And then you can use that rate to actually determine how long ago that thing must've died. So the rate at which this happens, so the rate of carbon decay, is essentially half disappears, half gone, in roughly 5, years.

And this is actually called a half life. And we talk about in other videos. This is called a half life. And I want to be clear here. You don't know which half of it's gone. It's a probabilistic thing.

You can't just say all the carbon's on the left are going to decay and all the carbon's on the right aren't going to decay in that 5, years.

write the nuclide symbol for carbon 13 dating

So over the course of 5, years, roughly half of them will have decayed. Now why is that interesting? Well, if you know that all living things have a certain proportion of carbon in their tissue, as kind of part of what makes them up, and then if you were to find some bone-- let's just say find some bone right here that you dig it up on some type of archaeology dig. And you say, hey, that bone has one half the carbon of all the living things that you see right now.

It would be a pretty reasonable estimate to say, well, that thing must be 5, years old. Even better, maybe you dig a little deeper, and you find another bone. Maybe a couple of feet even deeper.

Carbon 14 Dating Problems - Nuclear Chemistry & Radioactive Decay

So how old is this? But that's not what's relevant here. Let's say we have a collection of atoms. And normally when we have any small amount of any element, we really have huge amounts of atoms of that element. And we've talked about moles and, you know, one gram of carbon I'm sorry, 12 grams-- 12 grams of carbon has one mole of carbon in it. One mole of carbon And what is one mole of carbon? This is a ginormous number. This is more than we can, than my head can really grasp around how large of a number this is.

And this is only when we have 12 grams. For example, one kilogram is about two pounds. So this is about, what? I want to say [? And pounds is obviously force. You get the idea. On Earth, well anywhere, mass is invariant. This is not a tremendous amount. So with that said, let's go back to the question of how do we know if one of these guys are going to decay in some way. And maybe not carbon, maybe we're talking about carbon or something. How do we know that they're going to decay?

And the answer is, you don't. They all have some probability of the decaying. At any given moment, for a certain type of element or a certain type of isotope of an element, there's some probability that one of them will decay. That, you know, maybe this guy will decay this second. And then nothing happens for a long time, a long time, and all of a sudden two more guys decay.

And so, like everything in chemistry, and a lot of what we're starting to deal with in physics and quantum mechanics, everything is probabilistic. I mean, maybe if we really got in detail on the configurations of the nucleus, maybe we could get a little bit better in terms of our probabilities, but we don't know what's going on inside of the nucleus, so all we can do is ascribe some probabilities to something reacting.

Now you could say, OK, what's the probability of any given molecule reacting in one second? Or you could define it that way. But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So what we do is we come up with terms that help us get our head around this. And one of those terms is the term half-life.

And let me erase this stuff down here. So I have a description, and we're going to hopefully get an intuition of what half-life means.

So I wrote a decay reaction right here, where you have carbon It decays into nitrogen And we could just do a little bit of review. You go from six protons to seven protons. Your mass changes the same. So one of the neutrons must have turned into a proton and that is what happened. And it does that by releasing an electron, which is also call a beta particle. We could have written this as minus 1 charge. It does have some mass, but they write zero. This is kind of notation.

So this is beta decay. Beta decay, this is just a review. But the way we think about half-life is, people have studied carbon and they said, look, if I start off with 10 grams-- if I have just a block of carbon that's 10 grams. If I wait carbon's half-life-- this is a specific isotope of carbon. Remember, isotopes, if there's carbon, can come in 12, with an atomic mass number of 12, or with 14, or I mean, there's different isotopes of different elements.

And the atomic number defines the carbon, because it has six protons. Carbon has six protons. But they have a different number of neutrons. So when you have the same element with varying number of neutrons, that's an isotope.

So the carbon version, or this isotope of carbon, let's say we start with 10 grams. If they say that it's half-life is 5, years, that means that if on day one we start off with 10 grams of pure carbon, after 5, years, half of this will have turned into nitrogen, by beta decay. And you might say, oh OK, so maybe-- let's see, let me make nitrogen magenta, right there-- so you might say, OK, maybe that half turns into nitrogen.

And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen?

And how does this half know that it must stay as carbon? And the answer is they don't know. And it really shouldn't be drawn this way. So let me redraw it. So this is our original block of our carbon What happens over that 5, years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points. So if you go back after a half-life, half of the atoms will now be nitrogen. So now you have, after one half-life-- So let's ignore this.

So we started with this. All 10 grams were carbon. This is after one half-life.

  • Half-life and carbon dating
  • Carbon 14 dating 1

And now we have five grams of c And we have five grams of nitrogen Let's think about what happens after another half-life. So if we go to another half-life, if we go another half-life from there, I had five grams of carbon So let me actually copy and paste this one. This is what I started with.