Nuclear fusion | Physics | Khan Academy

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 come from? Well, they are forged 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 nuclei. For example, if you take a 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 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.

This reaction is not really complete, and you will see in a second why. But first of all, you can see how we can write this out, right? Because you have 1 + 1, you should have two protons over here. And since there are two particles—sorry, 1 plus 2—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. You see lighter nuclei fuse to form a heavier, larger nucleus.

Let's take another example: what if we have two helium-4 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?

Alright, so because there are two protons here and two protons here, totally we should have four protons. And since there are four and four particles total, we should have eight particles. 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. If you were to show the protons and neutrons, it will look somewhat like that. You can again see lighter nuclei, smaller nuclei, fuse together to form heavier, larger nucleus.

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 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.

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 it 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 would 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—what's happening inside the core of our Sun right now.

Where does the Sun and all the stars get their energy? Via 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 will find inside the core of a star. You have very high temperature, and there's extremely high pressure, which packs them and makes them zip along with very high speed. That's why fusion can happen inside the cores of stars, 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 probably already 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. 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. Alright, for this, I want us to compare the mass of the reactants with the mass of the products. Now 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; the mass of the product is actually less than the mass of the reactants over here.

How does that make any sense? If you're wondering, we need to resort to one of the most famous equations of physics, E=mc². 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; it 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 c², boom—you will 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 c², and boom—you get the energy that is released!

Now, as mentioned earlier, if a nuclear fusion reaction gives you a product that is less stable than the reactants themselves, then it will have more energy. In that case, you will find that the mass of the product would be larger than the mass of the reactants, 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=mc² when I was learning this. First of all, I was like, "Wait a second, why doesn't this apply to chemical reactions? Even though there, if energy is lost or absorbed, shouldn't that also produce the difference in masses of the products and reactants?" It turns out it happens, but the energies that we're dealing with are so incredibly tiny over there that we just ignore it.

So E=mc² is implied even in chemical reactions; the mass of the product and the mass of the reactants are not the same, but it's so small that we neglect it. E=mc² is universal; it's applied everywhere. It's just that it becomes more prominent when it comes to nuclear reaction reactions.

Secondly, I used to wonder: light has energy, but it does not have any mass. Light has zero mass, so isn't the equation violated? Well, that's where I realize that this equation does not really work for light. In fact, 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 light can never be at rest. And that's why E=mc² doesn't work for light.

Anyhow, 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, where did the deuterium come inside our Sun? Shouldn't we be getting helium-4? Why are we getting helium-3?” That's a good question because it turns out this is not the only reaction.

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. Clearly, there must be a reaction that must be happening before that is producing the deuterium nucleus, right? That reaction is you have just two protons that fuse together to get a nucleus with two protons. But you can feel in your bones that this is extremely unstable. There are no neutrons over here. This nucleus is not going to stay; it will instantly split back into the two protons. So no luck over here.

So the 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 tiny chance that once they fuse together, this proton can actually undergo beta decay and convert into a neutron. We've talked about beta decay 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. If you write the equation for this, well, it's going to look like this: you have two protons (hydrogen nuclei) fusing to get a deuterium nucleus. 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 will now make sense that in order for a deuterium nucleus to be formed, you'll have to wait a long time.

In fact, calculations show that you'll 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 time scales over here—it's insane!

Anyhow, 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 will 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 happen, but what's important is the core temperature will rise, and then it'll start fusing helium into heavier nuclei. In fact, it will fuse helium into carbon.

But after that, our Sun will just not have enough temperature to fuse carbon into heavier nuclei—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 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 nuclei together, the product will be less stable, which means it will 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 an 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 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 supernova explosion. And that's how all the heavy elements that were ever produced inside the core of this star finally get unlocked, and they can now go through the cosmos.

They can eventually land up on a planet like Earth and eventually find their way inside your body and my body. Now, since supernova produces one of the 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, it turns out, but supernova 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.