Lesson Video: Alpha Decay Physics

In this lesson, we will learn how to solve nuclear equations involving alpha decay.


Video Transcript

In this video, we’re talking about alpha decay. As we’ll see, alpha decay is a radioactive process where the nucleus of an atom, its core, emits a certain type of particle. A good starting point for talking about alpha decay is the nucleus of an atom.

If we think about it, atomic nuclei are a bit odd. After all, we know that a nucleus has no negative charges in it. So it’s just made up of positive charges, what we’ve colored gold, and neutral charges, what we’ve colored blue. But here’s the thing. If we took two of these positive charges — we call them protons — and try to bring them close together, what would happen?

We know that because both these particles have the same type of electric charge, they would push one another away. They would repel. But then looking over at the nucleus, we see it consists of lots of positive charges clumped close together. Since all these charges are pushing one another apart, it seems strange that a nucleus is able to form in the first place.

To see how this works, to see how atomic nuclei can form and be stable at all, we can perform a bit of an experiment. Let’s say we take our two positive charges, our protons, and we start with them very far apart from one another. At this distance, these like charges still repel one another. But the force isn’t very strong. Let’s say further that we fix the charge on the left in place so it can’t move. And then we start to apply a force to the charge on the right. What we do is we start pushing the charge on the right towards the charge on the left. We start going against the electrostatic force.

Doing this takes work, but it is possible. By pushing hard enough, we’re able to move this charge farther and farther to the left. As we do, the repulsive force between the charges gets stronger and stronger and stronger. But we keep it up until eventually, after exerting an unbelievable amount of force to bring these charges this close together, we notice something interesting happen.

Suddenly, when these charges are quite close, the charge on the right snaps to the charge on the left, almost like they’re magnetically attracted. Surprised by this, we let off the application of force and we see the charges stay as they are. They’re not repelling. What’s going on?

Well, it turns out we discovered one of the fundamental forces of the universe. This force has got the name “the strong nuclear force.” Here’s what’s very interesting about it. This force only operates over very short distance scales. That’s why when our protons were very far apart, we didn’t notice this force. It really wasn’t active at that point. Only when these tiny particles got very close to one another, only when they were about one diameter away from each other, does this strong nuclear force kick in. But when it does, it’s powerful. It’s actually the most powerful force known.

As we can see, it’s even strong enough to overcome the repulsion that these like-charged objects naturally experience. It’s this force, the strong nuclear force, that’s responsible for holding atomic nuclei together. If it was just up to the electrostatic force, the nuclei would basically explode, as all the positively charged protons push one another apart.

So when it comes to atomic nuclei, we have a balance of forces. There’s this strong nuclear force, which as we mentioned only applies over very small distances, and the electrostatic force, which are pushing against one another. The strong nuclear force attracts, trying to keep the nucleus intact. And the electrostatic force competes with this. This competition between forces can sometimes create an unstable situation.

Consider again our two positive charges, our protons. Let’s say we were able to disattach these two charges and then push the one on the right away from the one on the left. This time, we’ll be working against the strong nuclear force. When the two charges are about this far apart, the two forces acting on them, the strong nuclear force to attract and the electrostatic force to repel, are roughly in equilibrium. But here’s the thing. It’s an unstable equilibrium.

If we move this proton just a tiny bit to the left, then the strong nuclear force would dominate and the two charges would snap together. But then if we moved it just a tiny bit to the right, the electrostatic force would win out and these two charges would fly apart. What we have then is a fairly delicate balancing act. And that’s just between two protons.

Now imagine we have a much more complicated nucleus with many protons and many neutrons. Depending on the number of protons and the number of neutrons that are in a nucleus, it’s possible for some of those particles that the force of repulsion becomes greater than the force of attraction. In that case, the nucleus becomes destabilized. When this happens, the nucleus is about to go through a process called nuclear decay.

Nuclear decay is the name we give to a process when the core of an atom, that is, the nucleus, loses energy. Now it seems to make sense that if a nucleus, like this one we have here, went through a decay process, what it will lose could only be either protons or neutrons. That’s what the nucleus is made of. And while that is possible, it’s possible for protons and neutrons to break off from this nuclear ball.

Nuclear decay can happen in other ways too. That’s why we say it involves the loss of energy. This energy might involve mass or it might not. For our purposes though, we’re talking about a specific type of nuclear decay, called alpha decay. This kind of decay, this kind of nuclear loss, was first discovered in the late 1800s. And it was the first type of radioactive decay observed.

What researchers observed is that, in this process, a nucleus emitted a clump of matter that had two protons and two neutrons. And that of course meant that the emitting nucleus had two fewer neutrons and two fewer protons to it. This little bunch of matter, the two protons and the two neutrons, were given the name “alpha particle.” And the reason for the name is, since this was the first type of radioactive decay observed, the researchers just went to the first letter in the Greek alphabet, alpha. And they called it an alpha particle.

As we mentioned, these alpha particles consist of two protons, two positively charged particles, and two neutrons, particles with no charge. Something interesting about these particles is that if we went over the periodic table of elements and we looked up what element is number two, the element that has two protons in its nucleus, we would see that it’s helium. Helium is the element with an atomic number of two.

Moreover, it’s possible for a helium atom to have a nucleus with two neutrons in it, giving it a mass number of four. In other words, a helium nucleus is often made up of two protons and two neutrons. That’s the exact recipe for an alpha particle. Because of this, alpha particles are sometimes referred to as helium nuclei. They’re the same thing.

Now whenever an atomic nucleus emits an alpha particle, that’s called alpha decay. In this process, we could say that there’s a before and an after. The initial or the before instant is the time before the alpha particle is emitted when the nucleus is its original size. But then after the alpha particle is emitted, we can say we now have two pieces, where before we had one.

The first piece is the new nucleus that’s lost an alpha particle. And the second piece is the alpha particle itself. We could call these two pieces the products of a nuclear decay reaction. And that brings us to something very useful about nuclear decay processes.

Often we can write these processes as though they were equations. To see how this is so, let’s consider an example of this decay process. Say that we have a sample of thorium-228. We can see that these thorium atoms have 90 protons in the nucleus. And since this number, 228, represents the number of protons plus neutrons, then that must mean that we have 228 minus 90 or 138 neutrons in the nucleus of these thorium atoms.

Now all this would be well and good and these thorium atoms will continue on as they are for millions and millions of years except for one thing. These atoms are unstable. In the nuclear core of these atoms, there’s a push and pull going on between the strong nuclear force and the electrostatic force. And eventually, when the conditions are right, for some of those particles in the nucleus, the electrostatic force wins out. When that happens, these thorium atoms decay. They lose some of their energy. And they decay into a couple of products. One product is the particle they emit, in this case an alpha particle.

The symbol for an alpha particle is just the Greek letter 𝛼. And then to show that an alpha particle has two protons and two neutrons, we put a two down at the atomic number and a four for the mass number. That alpha particle is one of the products, but we know it’s not the only one. We can see that when a nucleus emits an alpha particle, there’s still some resulting nucleus left after the emission.

In the case of this decay of thorium into an alpha particle and another element, that other element is radium. Radium has 88 protons in its nuclear core. And it has 224 minus 88, which is equal to 136, neutrons in its nucleus. This is an example of a nuclear decay equation. And in fact, there’s a good reason that we call it an equation.

At this point, it’s helpful to recall that a general principle in physics is that energy is conserved. That is, within a closed system, the energy at any one time within that system is the same as the energy at any other time within that same system. If our system in this case consists of our decaying thorium atoms and the products from that decay, then we know that the total energy before the decay happens must equal the total energy after it occurs.

And in this instance, the conservation of energy is expressed as the conservation of mass number as well as atomic number. In other words, if we add up the atomic numbers of everything on the left-hand side, that will have to equal the sum of all the atomic numbers of everything on the right-hand side. Likewise, if we add up the mass numbers on the left, that has to equal the sum of the mass numbers on the right. We see that it does. But what we’re saying is that’s generally true whenever the products of a nuclear reaction are purely protons and neutrons, like we have here in our alpha particle and radium atoms.

So whenever we have an alpha decay process like this, where one kind of element decays into an alpha particle plus another type of element, there are two equations we can write. We can write an atomic number equation. In this case, that 90 is equal to two plus 88. And we can also write a mass number equation, that the mass number on the left side is equal to the sum of the mass numbers on the right side. Since in this case we were given the mass numbers and the atomic numbers for everything involved, these two equations probably seem a bit obvious.

But let’s say that we weren’t given all this information. Let’s say instead that we were told that these thorium atoms decayed into an alpha particle and radium with some number, 𝑁, as its mass number. In that case, we could come up here to our mass number equation and say that 228, the mass number of thorium, is equal to four, the mass number of the alpha particle, plus 𝑁, the mass number of radium. And then using this equation, we could solve for 𝑁. And then using the atomic number equation, the same thing would work if one of the atomic numbers was unknown. Knowing all this about alpha decay, let’s get some practice with these ideas through an example.

The following nuclear equation shows how an isotope of curium decays to plutonium via alpha decay. What are the values of 𝑝 and 𝑞 in the equation?

Taking a look at this equation, we see that curium, symbolized Cm, is decaying into plutonium, Pu, plus an alpha particle, symbolized with the Greek letter 𝛼. This decay event means that the curium nuclei has become unstable. And it’s split up into two pieces, the plutonium plus the alpha particle. We see that, for curium as well as for plutonium, both the atomic number as well as the mass number is given. But for the alpha particle, instead of those numbers, we have a 𝑞 and a 𝑝, respectively. It’s those values we want to solve for. And as we’ll see, there are two ways of going about doing this.

The first way is to recall what an alpha particle is, what it consists of. An alpha particle, the particle emitted in an alpha decay event, consists of two protons as well as two neutrons. That means if we were to represent an alpha particle as though it was its own atomic element, we would write its atomic number, the number of protons it has, two, and then its mass number, the sum of protons as well as neutrons in the particle, four. These numbers are true for any alpha particle. They always have two protons and two neutrons.

The alpha particle involved in this equation is the same way. It also has two protons and two neutrons. This will indicate to us that 𝑞 is equal to two and that 𝑝 is equal to four. This is one way to find the answer to this question. But as we’ll see, there’s another way, even if we didn’t recall this about an alpha particle.

This second approach involves looking at these values, 𝑝 and 𝑞, in terms of the equation that they’re part of. This type of nuclear decay equation, where one kind of element decays into another element plus an alpha particle, involves what we could call the conservation of atomic number — that’s this number here to the lower left — as well as the conservation of mass number — that’s this number here to the upper left. In other words, the atomic number and the mass number on the left of this equation equal the sum of the atomic numbers and mass numbers on the right of the equation. This means there are two separate equations we can write down to help us solve for 𝑝 and 𝑞.

First, we can write down the atomic number equation. Since atomic number is conserved across this equation, it means that 96, the atomic number of curium, is equal to 94, the atomic number of plutonium, plus the atomic number of the alpha particle. That’s 𝑞. And then, likewise, for the mass numbers of these constituents, the mass number of curium, 247, is equal to the mass number of plutonium, 243, plus the mass number of the alpha particle, 𝑝. We can use these two separate equations to solve for 𝑞 and to solve for 𝑝. 𝑞 is equal to 96 minus 94, or two. And 𝑝 is equal to 247 minus 243, or four. Whichever of these approaches we use, we end up finding that 𝑝 is equal to four and 𝑞 is equal to two.

Let’s take a moment now to summarize what we’ve learned about alpha decay. First off, in this lesson, we saw that, due to competing forces, specifically the strong nuclear force competing against the electrostatic force, atomic nuclei can become unstable. An unstable atomic nucleus can decay. This is a process that occurs when that nucleus loses mass or energy or both. A certain type of decay, called alpha decay, involves a nucleus emitting a particle that has two protons and two neutrons.

We saw that this particle is called an alpha particle and that it’s the same thing as the nucleus of a helium atom. That is, it has two protons and two neutrons in it. And finally, we saw that, in nuclear decay equations, such as equations involving alpha decay, the emission of an alpha particle, energy is conserved.

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