Half-life

- [Narrator] This is a Neanderthal skull. Neanderthals are extinct species of humans and we believe they went extinct about 35 to 40,000 years ago. And this is Earth and we believe Earth to be about four and a half billion years old. But my question was always, "How do we know these things? "How do we figure these things out?" Turns out one common method is radiometric dating where we make use of radio isotopes to figure this out. But how does that work? How do you use radioactivity to figure out how old something is? Well, let's find out. Carbon-14 is a radio isotope of carbon, so it decays into a more stable isotope nitrogen-14. Now if you take any amount of carbon-14 you want, take any amount you want. Let's just take some number, nice number, 100 grams, let's say. Now, as time passes by, the atoms will start decaying and so, the amount of carbon-14 that you have will start reducing, isn't it? Now, it turns out that after about 5,730 years, 50 grams of carbon-14 would've decayed to nitrogen-14 and only 50 grams is left with you. Now, my question to you is what do you think will happen if we wait for another 5,730 years? My intention says it should now go to zero. All of the carbon-14 should decay. I mean, makes sense, right? In the first phase, in the first 5,730 years, 50 grams got decayed. Now we wait for the same amount of time, another 50 gram would decay. So, obviously, it should go to zero, but turns out that's not what happens. Instead, we find that now half of this amount gets decayed. So from 50 grams, 25 gram get decayed, and we're left with another 25 grams. And the same thing continues. If you wait for another 5,730 years, half of this value gets decayed and so on and so forth. That's how radioactivity proceeds. So, this means regardless of whatever amount of carbon-14 you have with you, it doesn't matter what amount you have, but if you wait for 5,730 years, it'll reduce to half its value, half of whatever you have right now. And therefore, that is called, that number is called half life. It's a number that tells you how much time you have to wait for 50%, half of the amount of stuff that you have, to decay. It could be half of the mass that you have to decay. It could be half of the number of atoms that you currently have to decay, number of moles, whatever. It's half of the amount of stuff, how much time you have to wait for half this amount of stuff to decay. Let's take another example. If you take uranium-238, turns out that it is a radioisotope, and turns out that whatever the hotter isotope you get after the decay also undergoes another radioactive decay and there's a chain like that, but eventually it ends in lead. Now, that's besides the point. What's important is the half-life of uranium-238 happens to be about four and a half billion years. Now, what does that mean? Well, what it means is that if you take some amount of uranium-238 with you, again, it doesn't matter what amount you take with you right now, let's take some random 68 grams. You have 68 grams of uranium-238 with you. Now, if you wait for four and a half billion years, that amount will reduce to half. What happens if you wait another four and a half billion years? Well, again, that amount will not vanish now. Again, it will reduce to half and that'll keep on happening. Half-life. So, each radio isotope will have its own half life. But the big question is why does radioactivity proceed like this? To gain some insights into this, let's play a game. Let's put 100 million people in a room and decide to toss a coin every minute. Now, if you get a tail, you're done, the game is over, you leave the room, but if you get a head, you stay in the room, wait for another minute and toss a coin again. And you keep on doing this. So, my question to you is what's gonna happen after a minute? We start the game, we wait for a minute, everybody tosses a coin. How many people will be left in the room after one minute? Well, you would say that tossing a coin is a random event, so there's a 50% chance of getting a heads or tails. If I focus on any one individual, I have no clue whether that person is going to get a heads or not, heads or tails. But since I have 100 million people, statistics comes into play. So, 50% of this group is gonna get heads and about 50% will get tails. Which means half of them will stay in the room and other half would have left. So, we would have 50 million in the room, isn't it? Now, we continue. We wait for one more minute. What do you think is gonna happen? Do you think now all 50 million would leave the room? No, you would say, "Hey, the same thing's gonna happen again" because again, 50% of you know there's a random chance, 50% of them will get heads, 50% of them will get tails. It's again, only 50% of this will stay. That is 25 million will stay and the game will continue like that. Do you see a parallel between these two? I mean, because tossing a coin is almost a random event, if I were to focus on one specific individual, that person might survive the game for another 100 tosses or that person might leave the room the very next minute. I have no clue. I cannot comment on what happens individually, but because we have 100 million of them, statistics becomes more significant. I can tell that 50% of this must keep decaying, 50% of them must leave. Something very similar is happening over here. If you take a single atom, there's no way to predict what's going to happen. It might decay the very next second or it may not decay for another billion years. There's absolutely no way to talk about that. But if you take billions and trillions and trillions of atoms together, if you take a lot of them together, then, statistics become significant. And so, in four and a half billion years, if half of them decay, well then, in another four and a half billion years, again, only half of them must decay, and that's why it must continue. Doesn't that make sense? Think about this for a while. The key over here is that radioactivity is a random process and that's why the chances of a radioactive atom decaying at any given moment is 50-50. There's a 50% chance it'll decay, 50% chance it'll not decay. This is the reason why the statistics works out, and by the way, there's absolutely no way you can influence those chances. There's nothing you can do that will, say ,force it to decay or will stop it from decaying. All you can do is just sit back and watch it. This also means that the half-life of a radioactive sample is fixed. For example, carbon-14 always has a half life of 5,730 years period. It doesn't matter how much carbon-14 you take, under what conditions you take it, none of that matters. Similarly, half-life of uranium-238 is always going to be four and a half billion years, done. And that's awesome, because not just by looking at half-lifes, you can comment about which isotopes are more radioactive. I mean, which of these two do you think is more radioactive? Well, carbon-14 only takes about 5,700 years to decay to half the value. But uranium takes about four and a half billion years. So, you can immediately see because it has a shorter half-life, carbon-14 must be more radioactive. Shorter the half-life, the quicker it decays, more radioactive something is. There are isotopes which have half-lifes in mere seconds. Anyways, now there's one big difference between the game that we played and how radioactivity unfolds in reality. What's that difference? Well, let me just move this thing to the side. So, if we go back to our game that we played and we try to draw a graph. On the Y axis, we'll plot the number of people who are remaining, and on the X axis we'll draw the number of half-lifes. Initially we had 100 million people to begin with, so 100% of them were remaining, and they stayed in the room for about a minute. Then they tossed a coin and then, immediately that number reduced to half, half of it, 50%. And then again, that stayed in the room for a minute, and then again, it immediately reduced to half and that kept on going, right? Well, the difference is in actual radioactivity, it doesn't happen like this. It's not like the 68 grams will stay 68 grams for four and a half billion years and then instantly reduce to 34 grams like over here. Instead, that radioactivity is a continuous process that will be continuously the amount of isotope that you have will continuously decay. This number will continuously reduce. And so, the actual graph that you'll get will be more of a curve that looks like this. But the point is after, if you wait for one half life, which could be 5,730 years for carbon-14 or four and a half billion years for uranium-238. But if you wait for one half life, look, the number reduces to 50%. And then if you wait for the second half life, another half life, the number reduces to 50% of that, which is 25% and so on and so forth. This now brings us to our original question. How do you figure out age of things? For example, how do you figure out how old Earth is? Geologists use what we call zircon crystals. I'll tell you what's so special about these crystals. They absolutely hate lead. We'll not worry about why that is the case, but that turns out to be true. But let's say you find a zircon crystal and inside you'll find some traces of uranium and some lead as well. And just to keep, take simple numbers, I'm just taking 10 milligrams and 10 milligrams over here, okay? But then you question like, where did this lead come from? You realize, hey, a lot of this uranium is radioactive, and so, this lead must have come from the decay of uranium. There is no other way this lead could have come over here. And so, this means you conclude that when this crystal was formed long time ago, all of those atoms of lead must have been uranium to begin with. And then because of the decay they turned into lead. And that's how you conclude that probably when the crystal was formed, you must have had about 10%, 20 milligrams of uranium. But wait a second, look at what this means. This means that about half the uranium atoms have decayed. And since we know that the half life of uranium is always four and a half billion years, you say, "Aha, about four and a half billion years "must have passed since the time that crystal was formed." Now, I know this is an oversimplification, but you get the idea, right? Now, to age the entire Earth, well, we look at a lot of such rocks, which we believe to be very old, and we found that almost a lot of the old ones date back to about four and a half billion years. And that's how we concluded that maybe Earth was formed about four and a half billion years ago. Okay, what about the Neanderthal bones? We used a very similar technique, but instead of using uranium, because uranium, the decay happens over a much longer time span. We use carbon dating. All living organisms, including you and me, have radioactive carbon-14 inside of us. And so, by looking at how much carbon-14 is left, again, this is an oversimplification, but by looking at that, we can estimate how long ago that person lived. This is why I feel radioactivity is incredibly cool.