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如何通过钾-氩测年法确定上古火山岩以及埋没在其中物质的年份. Sal Khan 创建




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 we know if an atom has 19 protons it is going to be potassium now we also know that not all members of or not all of the atoms of a given element have the same number of neutrons and when 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 potassium can come in a form that has exactly 20 neutrons and we call that potassium we call that potassium 39 and 39 this mass number it's a count of the 19 protons 19 protons plus 20 neutrons and this is actually the most common isotope of potassium it accounts for 93.3 I'm just rounding off this is 93 0.3% 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 in the nineteen or 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 percent of the potassium on the planet and then you have a very scarce isotope of potassium called potassium 40 potassium 40 Curley has 21 neutrons it's very very very very scarce it accounts for only 0.01 1 7 percent 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 it's percent 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 five 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 so every 1.25 billion years let me write it like this 1.25 billion years that's it's half-life so 50 percent of any given sample will have decayed and 11 percent 11 percent will have decayed into argon-40 11 percent will have decayed into argon-40 so argon is right over here it has 18 protons so when you see 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 have somehow turned into a neutron it actually captures one of the inner electrons and it be and then emits other things and I won't go into all the quantum physics of it but turns into argon-40 and 89 percent 89 percent to turn into calcium 40 calcium 40 and you see calcium on the periodic table right over here is 20 protons so this is a situation where one of the neutrons turns into a protons 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 this part right over here because what's cool about argon and we studied this a little bit in the chemistry playlist it is a noble gas it is unreactive and so when it is when it is embedded in something that's in a liquid state it'll kind of just bubble out it's not bounded 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 is it erupts and you have all of this lava flowing all of this lava and while the lava that lava will contain some amount of potassium-40 and actually it'll already contain some amount of argon-40 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 let's imagine this lava right over here it's a bunch of stuff it's a bunch of stuff right over here but in that stuff it is going to have I'll do I'll do the potassium-40 in 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 just not you know I may be overdoing 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 so it might have already have some argon-40 in it just like that but argon-40 is a noble gas it's not gonna bond to anything and while this lava is in a liquid state it's going to be able to bubble out 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 or just I should say evaporate a little just it'll just bubble out essentially because it's not bonded to anything and it's so it'll just it'll just seep out 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 by the time this this lava has hardened into volcanic rock and I'll do that let me do that a volcanic rock in a different color by the time it has hardened into a 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 you're going to be left with potassium-40 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 at the volcanic event resets the amount of car argon-40 so at future date and so right when the event happened you shouldn't have any argon-40 right when it when that when that lava actually you know it becomes a solid and so if you if you fast forward to some future date and if you look at this sample let me copy and paste it so let me copy and let me paste it so if you fast forward to some future date if you fast forward to some future date and you see that there is some argon-40 there you see that there's some argon-40 in that sample you know you know and you know this is volcanic rock you know that it was due to some previous volcanic event you know that this argon-40 this argon-40 is from decayed potassium-40 it's from decayed decayed potassium-40 and it you know that it it has decayed since that volcanic event because if it was there before it would have seeped out so there the only way that this would have been able to get trapped is if while it was liquid it would seep out but once it's solid it can get trapped inside the rock and so you know that the only time that's 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 you know for one of for every one of these argon-40 s because it's only 11% of the decay products or argon-40 for every one of those you must have had you must have on the order of about nine calcium forties that came from that that that also decayed and so for every one of these argon-40 s you know that there must have been ten 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 you know volcanic volcanic eruptions aren't happening every day but if you start looking over millions and millions of years on that timescale they're actually happening reasonably frequent and so if you dig in the ground 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 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 and let's say that this one over here so they're all going to have a certain amount of the hassium 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 versus what you are using the ratio of the potassium-40 left to what you know was there before you say that this 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 150 million years before the present and let's say you feel pretty good this soil hasn't been dug up and mixed or anything like that it looks like it's been pretty untouched when you when you look at these soil samples right over here and let's say you see some fossils let's see let's say you see some fossils in here then even though carbon-14 dating is kind of useless but really when you get beyond 50 thousand 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 is between a hundred million and 150 million years old yes 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 it allows you to relatively date things in between those layers 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