Potassium-argon (K-Ar) dating

We know that an element is defined by the number of protons it has. For example, potassium. We look at the periodic table of elements. And I have a snapshot of it, of not the entire table but part of it here. Potassium has 19 protons. And we could write it like this. And this is a little bit redundant. We know that if it's potassium that atom has 19 protons. And we know if an atom has 19 protons it is going to be potassium. Now, we also know that not all of the atoms of a given element have the same number of neutrons. And when we talk about a given element, but we have different numbers of neutrons we call them isotopes of that element. So for example, potassium can come in a form that has exactly 20 neutrons. And we call that potassium-39. And 39, this mass number, it's a count of the 19 protons plus 20 neutrons. And this is actually the most common isotope of potassium. It accounts for, I'm just rounding off, 93.3% of the potassium that you would find on Earth. Now, some of the other isotopes of potassium. You also have potassium-- and once again writing the K and the 19 are a little bit redundant-- you also have potassium-41. So this would have 22 neutrons. 22 plus 19 is 41. This accounts for about 6.7% of the potassium on the planet. And then you have a very scarce isotope of potassium called potassium-40. Potassium-40 clearly has 21 neutrons. And it's very, very, very, very scarce. It accounts for only 0.0117% of all the potassium. But this is also the isotope of potassium that's interesting to us from the point of view of dating old, old rock, and especially old volcanic rock. And as we'll see, when you can date old volcanic rock it allows you to date other types of rock or other types of fossils that might be sandwiched in between old volcanic rock. And so what's really interesting about potassium-40 here is that it has a half-life of 1.25 billion years. So the good thing about that, as opposed to something like carbon-14, it can be used to date really, really, really old things. And every 1.25 billion years-- let me write it like this, that's its half-life-- so 50% of any given sample will have decayed. And 11% will have decayed into argon-40. So argon is right over here. It has 18 protons. So when you think about it decaying into argon-40, what you see is that it lost a proton, but it has the same mass number. So one of the protons must of somehow turned into a neutron. And it actually captures one of the inner electrons, and then it emits other things, and I won't go into all the quantum physics of it, but it turns into argon-40. And 89% turn into calcium-40. And you see calcium on the periodic table right over here has 20 protons. So this is a situation where one of the neutrons turns into a proton. This is a situation where one of the protons turns into a neutron. And what's really interesting to us is this part right over here. Because what's cool about argon, and we study this a little bit in the chemistry playlist, it is a noble gas, it is unreactive. And so when it is embedded in something that's in a liquid state it'll kind of just bubble out. It's not bonded to anything, and so it'll just bubble out and just go out into the atmosphere. So what's interesting about this whole situation is you can imagine what happens during a volcanic eruption. Let me draw a volcano here. So let's say that this is our volcano. And it erupts at some time in the past. So it erupts, and you have all of this lava flowing. That lava will contain some amount of potassium-40. And actually, it'll already contain some amount of argon-40. But what's neat about argon-40 is that while it's lava, while it's in this liquid state-- so let's imagine this lava right over here. It's a bunch of stuff right over here. I'll do the potassium-40. And let me do it in a color that I haven't used yet. I'll do the potassium-40 in magenta. It'll have some potassium-40 in it. I'm maybe over doing it. It's a very scarce isotope. But it'll have some potassium-40 in it. And it might already have some argon-40 in it just like that. But argon-40 is a noble gas. It's not going to bond anything. And while this lava is in a liquid state it's going to be able to bubble out. It'll just float to the top. It has no bonds. And it'll just evaporate. I shouldn't say evaporate. It'll just bubble out essentially, because it's not bonded to anything, and it'll sort of just seep out while we are in a liquid state. And what's really interesting about that is that when you have these volcanic eruptions, and because this argon-40 is seeping out, by the time this lava has hardened into volcanic rock-- and I'll do that volcanic rock in a different color. By the time it has hardened into volcanic rock all of the argon-40 will be gone. It won't be there anymore. And so what's neat is, this volcanic event, the fact that this rock has become liquid, it kind of resets the amount of argon-40 there. So then you're only going to be left with potassium-40 here. And that's why the argon-40 is more interesting, because the calcium-40 won't necessarily have seeped out. And there might have already been calcium-40 here. So it won't necessarily seep out. But the argon-40 will seep out. So it kind of resets it. The volcanic event resets the amount of argon-40. So right when the event happened, you shouldn't have any argon-40 right when that lava actually becomes solid. And so if you fast forward to some future date, and if you look at the sample-- let me copy and paste it. So if you fast forward to some future date, and you see that there is some argon-40 there, in that sample, you know this is a volcanic rock. You know that it was due to some previous volcanic event. You know that this argon-40 is from the decayed potassium-40. And you know that it has decayed since that volcanic event, because if it was there before it would have seeped out. So the only way that this would have been able to get trapped is, while it was liquid it would seep out, but once it's solid it can get trapped inside the rock. And so you know the only way this argon-40 can exist there is by decay from that potassium-40. So you can look at the ratio. So you know for every one of these argon-40's, because only 11% of the decay products are argon-40's, for every one of those you must have on the order of about nine calcium-40's that also decayed. And so for every one of these argon-40's you know that there must have been 10 original potassium-40's. And so what you can do is you can look at the ratio of the number of potassium-40's there are today to the number that there must have been, based on this evidence right over here, to actually date it. And in the next video I'll actually go through the mathematical calculation to show you that you can actually date it. And the reason this is really useful is, you can look at those ratios. And volcanic eruptions aren't happening every day, but if you start looking over millions and millions of years, on that time scale, they're actually happening reasonably frequent. And so let's dig in the ground. So let's say this is the ground right over here. And you dig enough and you see a volcanic eruption, you see some volcanic rock right over there, and then you dig even more. There's another layer of volcanic rock right over there. So this is another layer of volcanic rock. So they're all going to have a certain amount of potassium-40 in it. This is going to have some amount of potassium-40 in it. And then let's say this one over here has more argon-40. This one has a little bit less. And using the math that we're going to do in the next video, let's say you're able to say that this is, using the half-life, and using the ratio of argon-40 that's left, or using the ratio of the potassium-40 left to what you know was there before, you say that this must have solidified 100 million years ago, 100 million years before the present. And you know that this layer right over here solidified. Let's say, you know it solidified about 150 million years before the present. And let's say you feel pretty good that this soil hasn't been dug up and mixed or anything like that. It looks like it's been pretty untouched when you look at these soil samples right over here. And let's say you see some fossils in here. Then, even though carbon-14 dating is kind of useless, really, when you get beyond 50,000 years, you see these fossils in between these two periods. It's a pretty good indicator, if you can assume that this soil hasn't been dug around and mixed, that this fossil is between 100 million and 150 million years old. This event happened. Then you have these fossils got deposited. These animals died, or they lived and they died. And then you had this other volcanic event. So it allows you, even though you're only directly dating the volcanic rock, it allows you, when you look at the layers, to relatively date things in between those layer. So it isn't just about dating volcanic rock. It allows us to date things that are very, very, very old and go way further back in time than just carbon-14 dating.