Nuclear fusion

- [Instructor] We believe that after the Big Bang, the early universe contained mostly hydrogen, helium, and traces of lithium. But then how did the rest of the elements come by? For example, where did the oxygen that we are breathing right now or the calcium in our bones, where did they come from? Well, they are forced in nuclear fusion reactions that are happening inside the core of the stars. But what exactly is a nuclear fusion reaction? How do they forge heavier elements? And more importantly, if they're happening inside the star, how do they come out of it and find their way towards us? Let's find out. Nuclear fusion is a nuclear reaction in which smaller nuclei combine to make larger nucleus. For example, if you take proton, which is the nucleus of hydrogen, and combine it with deuterium, which is basically the isotope of hydrogen, it has one proton, that's why it's a hydrogen, but it also has one neutron along with it. Okay, so it's a heavier isotope of hydrogen. If you combine them together, you will get a helium nucleus, and this reaction is not really complete, and you'll see in a second why. But first of all, you can see how we can write this out, right? Because you have one plus one, you should have twp protons over here. And since there are two particles, sorry, one plus two, there are three particles, you should have three particles over here. So, just by keeping track of protons and neutrons, you can try to predict what that product is going to be. So, you see lighter nuclei fuse to form a heavier, larger nucleus, nuclear fusion. Let's take another example. What if we have two helium, four nuclei fusing together? Can you predict what would be the larger nucleus that we'll get over here? Why don't you pause and try? All right, so because there are two protons here and two protons here, total we should have four protons. And since there are four and four particles total, we should have eight particles. And so, the isotope I will get would have four protons, which is basically beryllium if you look at the periodic table, so we'll get beryllium-8 as our heavier nucleus. And if you were to show the protons and neutrons, it'll look somewhat like that. And you can again see lighter nuclei, small nuclei fuse together to form heavier, larger nucleus, nuclear fusion reaction. Now, I took these specific reactions because the product here turns out to be stable, but you can have nuclear reactions in which the products are not stable, which means they'll further undergo some kind of a radioactive decay. So, in general, we cannot predict the product that easily, but what's important is that under the right conditions and if you have the right nuclei, you can actually get energy out of it. And in fact, in both these cases, we will get energy. And this energy can be in the form of the kinetic energy of these products, or it can be of the kinetic energy of the decayed particles if these were unstable, it can also be taken away as the energy of photons, gamma radiation. In fact, that's what happens over here. And that's why I said it is an incomplete equation because turns out you actually do get gamma radiation over here. But don't expect to get energy by fusing any two nuclei together. You'll only get energy if the product is more stable compared to the reactants, and that happens to be the case over here. But now you might say, "Well, isn't this energy extremely tiny?" And you're right, the energy produced by each nuclear fusion reaction will be very tiny. But what if you consider billions and billions of reactions happening per second? Ooh, now you'll have a lot of energy coming out. And guess what? That's what powers up the stars, that's what's happening inside the core of our Sun right now. Where does the Sun and all the star get their energy? Why are nuclear fusion reactions? There are nuclear explosions happening in the core, lots and lots and lots of fusion reactions happening inside the core, that's what powers up our star. But this might now bring another question, why does it only happen inside the core of a star? I mean, why doesn't it happen all around us? Well, for that, you can thank or blame the positive charge of the protons inside the nucleus. Since nuclei are positively charged, they will repel, they have electrostatic repulsion against each other, which means fusing nuclei is not easy. If you want to fuse nuclei together, you need to first of all pack them very tightly and make sure they have incredibly high speeds so that they can overcome that repulsion, come close enough to be within the nuclear range. And then finally, if they're that close, then the nuclear force can take over and fuse them together. So, the conditions necessary are extreme, and that's the exact conditions you'll find inside the core of a star. You have very high temperature and there's extremely high pressure, which packs them and makes them, they're zipping along with very high speed. That's why fusion can happen inside the cores of a star. And it doesn't happen everywhere else. That's why it's also extremely hard to set up fusion reactions inside our labs. However, you already probably know that nuclear fusion is an active area of research because we want to figure out if we can somehow make use of this energy. And one aspect of this research is predicting how much energy a particular nuclear fusion reaction would yield. You know what's cool, folks? You can actually do that prediction just by using a pen and paper. That's right, it's possible to theoretically predict this. Let's see how. Let me clear the board. All right, for this, I want us to compare the mass of the reactants with the mass of the products. And my intuition says they should be exactly the same because we have two protons and one neutron on the left side, and you have two protons and one neutron on the right. But it turns out that's not true. Mass of the product is actually less than the mass of the reactant over here. How does that make any sense? If you're wondering. Well, we need to resort to one of the most famous equations of physics, E = mc square. You know what this equation is really telling us? It's telling us that energy and mass are equivalent to each other. Here's what I mean. You see, when you're measuring the masses, you're not just measuring the amount of stuff. Turns out according to this equation, you're also measuring the amount of energy content of that system. Now, in this reaction, some of that energy went out, right? Therefore, the energy content has reduced, and that's why the mass has reduced. So, even though the amount of stuff remains the same, because the energy has reduced, the mass has reduced. And now you can see that if more energy was given out in this reaction, this mass would be even smaller, and so the difference in the mass would be more. So, you can see, just by figuring out the difference in the mass, you can predict how much energy is given away. In fact, if you take the difference in the mass and multiply by c square, boom, you'll get the amount of energy that's given away. I find this so incredible. That means if you take any nuclear fusion reactions, and if you want to know how much energy it releases, just Google the masses of the reactants and the products, look at the discrepancy and multiply it by c square and, boom, you get the energy that is released. Now, as mentioned earlier, if nuclear fusion reaction gives you a product that is less stable than the reactant itself, then it'll have more energy. In that case, you'll find that the product of the mass, sorry, the mass of the product would be larger than the mass of the reactant. And you would say, "Okay, that's not a nuclear reaction we should go for because that's not giving energy, that's actually absorbing the energy." Now, before we go forward, let's address some questions that I had about E = mc square when I was learning this. First of all, I was like, "Wait a second, why doesn't this apply to chemical reactions? You went over there, if energy is lost or absorbed, shouldn't that also produce a difference in masses of the products and reactants?" Turns out it happens, but the energies that we're dealing with is so incredibly tiny over there that we just ignore it. So, E = mc square is implied, and even in chemical reactions, the mass of the product and the mass of reactants are not the same, but it's so small that we neglect it, we don't talk about it. E = mc square is universal, it's applied everywhere. It's just that it becomes more prominent when it comes to nuclear reactions. And therefore, when it comes to nuclear reactions, we talk about it. Secondly, I used to wonder, "Light has energy, but it does not have any mass, light has zero mass. So, that isn't the equation violated?" Well, that's where I realized that this equation does not really work for light. In fact, this equation, in this equation, E represents the rest energy, not the total energy. If you want to consider total energy, then the equation is actually bigger. So, when it comes to light, it doesn't have any rest energy because it light can never be at rest, and that's why E = mc square doesn't work for light. Anywho, going back to our original question, how do stars forge heavier elements? Well, our Sun right now is fusing protons into helium, but you might be looking at this and wondering, "Well, wait a second, wait a second. Where did the deuterium come inside our Sun? And shouldn't we be getting helium-4? Why are we getting helium-3?" That's a good question because turns out this is not the only reaction. So, just to appreciate what's going on inside our Sun right now because it's giving us life, let's just peek inside the sun. So, clearly there must be a reaction that must be happening before that is producing the deuterium nucleus, right? And that reaction is you have just two protons that fused together all to get a nucleus with two protons. (laughs) But you can feel in your bones that this is extremely unstable. There are no neutrons over here. This nucleus is not gonna stay put, it will instantly split back into the two protons. So, no luck over here. So, majority of the times, this is what will happen, they'll fuse and they'll split back, they'll fuse and they'll split back. But there's a very, very, very, very, very tiny chance that once they fuse together, this proton can actually undergo beta decay and convert into a neutron. We've talked about beta decays before, that's the way protons and neutrons can turn into each other. And when that happens, it's a very rare moment, but if that happens, then you get a deuterium nucleus. And if you write the equation for this, well, it's gonna look like this. You have two protons, hydrogen nuclei, fusing to get a deuterium. And this is the product of the beta decay, which you've seen before, don't worry too much about it right now. But it'll now make sense that in order for a deuterium nucleus to be formed, you have to wait a long time, right? In fact, calculations show that you have to wait billions of years on average for this to happen. However, what's more interesting is that once the deuterium nucleus is formed, it will instantly combine with one of the protons nearby within minutes or seconds to get the helium nucleus. So, these are average values, but think about the contrast of the timescales over here, it's insane. Anywho, in both cases we do get energy, but once the helium-3 is formed, the Sun will also fuse helium-3 nuclei together. And when that happens, we'll get, again, an unstable nucleus with four protons and two neutrons over here. But since it's incredibly unstable, it'll just release two protons away. And look, we finally get our helium-4 nucleus. This step also releases a ton of energy, and this is how our Sun, as we speak, is fusing protons into helium nuclei. Now, we also think that there are other sets of nuclear fusion reactions going on as well, but this is the dominant one. The last question we could ask is, what happens once the Sun runs out of all the protons once it has fused all the protons into helium? Well, a bunch of things happens, but what's important is the core temperature will rise and then it'll start fusing helium into heavier nucleus. In fact, it's fused helium into carbon, but after that, our Sun will just not have enough temperature to fuse carbon into heavier nucleus, it'll just stop over there. But if you have hotter, bigger, hotter stars, then the fusion process will just keep on happening. Carbon will fuse together to get even more heavier elements and this, the process will keep on happening, but not forever. Not forever, because once we reach iron, that marks the end of the fusion chain. Because you know what? Iron is one of the most stable elements in the universe, which means if you try to fuse two iron elements, iron nucleus nuclei together, the product will be less stable, which means it'll not give energy anymore, it'll absorb energy. This means once you have an iron core, the star runs out of an energy source. Well, what happens because of that? Well, there is insane crush of gravity because of the sheer mass of the star. Until now, the nuclear fusion reaction was able to balance it. But once the nuclear fusion stops because you can't fuse iron to get more energy, gravity wins. And as a result of that, the whole star collapses on itself and explodes into a super nova explosion. And that's how all the heavy elements that were ever produced inside the core of this star finally gets unlocked, and they can now go through the cosmos and they can eventually land up on a planet like Earth and eventually find its way inside your body and my body. Now, since super nova produces one of the most hottest places in our universe, I mean, the temperature we're talking about is just like we can't even talk about it anymore, it's so incredibly high that during that time even heavier nuclei are forced to fuse together. That's one of the ways in which we can get nuclei even heavier than iron. Of course, there are other ways turns out, but super nova is one of the ways in which that happens. But anyways, I think this is one of the reasons why we often say that you, me, and all of us are made of stardust because the elements that make us up were once a part of a dying star.