Lesson Video: Up Quarks and Down Quarks Physics

Video Transcript

In this video, we will be looking at particles known as quarks, otherwise pronounced quarks. These particles are the building blocks of matter, of the stuff that makes up our universe. We may already know that atoms are formed of protons, neutrons, and electrons. But it turns out that protons and neutrons, such as the ones in this diagram here, are themselves made up of even smaller particles. These smaller particles are the quarks that we’ll be discussing in this video. Now, protons and neutrons specifically are made up of two different kinds or flavours of quark. The up quark and the down quark. And yes, different kinds of quark really are known as different flavours of quark, delicious.

Now, the interesting thing about these quarks is that they are charged particles just like protons or electrons. But the really interesting thing about these quarks is that the magnitude or size of the charge that they carry is a fraction of the charge on a proton. Let’s start by recalling that protons, which in this case we’ll label as blue dots, have a charge of positive 1.6 times 10 to the power of negative 19 coulombs. In other words, protons are positively charged and they have this magnitude of charge in coulombs. Neutrons, which we’ll label in green, are neutral particles. Therefore, they carry a charge of zero coulombs. Electrons though are negatively charged particles. They carry a charge of negative 1.6 times 10 to power of negative 19 coulombs.

In other words, the sign on their charge is opposite to that of a proton. But both a proton and an electron have the same magnitude of charge. And until our understanding of quarks, it was thought that this magnitude of charge 1.6 times 10 to the power of negative 19 coulombs was the smallest charge that any particle could carry. Now by the way, this number, 1.6 times 10 to the power of negative 19, is quite a long and boring number to work with. So often, scientists will work in terms of relative charge, in other words, charge measured relative to the charge of a proton. And so we can start by working out the relative charge of a proton.

Remember, when measuring the charge of a proton relative to its own charge, therefore, the relative charge on a proton is positive one, positive because it has the same sign charge as a proton, surprise, surprise, and one because it has the same magnitude charge as a proton. Now, the reason that we do this is because the neutron still has a charge of zero relative to the charge of a proton and an electron has a charge of negative one, in other words, opposite sign but same magnitude. And using this relative charge system, the up quark actually has a charge of positive two-thirds. In other words, it has the same sign charge as a proton. It’s positively charged. But the magnitude or size of this charge is only two-thirds that of a proton.

Now in coulombs, that becomes two-thirds multiplied by 1.6 times 10 to power of negative 19 coulombs. But we’re not going to worry about that here. We’ll just keep it simple and work in terms of relative charge. So the up quark has a relative charge of positive two-thirds. The down quark, on the other hand, is negatively charged. But its magnitude is one-third that of the proton. Now as we said earlier, scientists initially thought that the smallest possible charge we could have on a particle was 1.6 times 10 to the power of negative 19 coulombs, whether positive or negative. And that’s why it was so shocking to think about particles that had a fraction of that charge, in other words, a charge smaller than 1.6 times 10 to the power of negative 19 coulombs.

But we’ll see why this was the case in a second. But first, let’s realise that these two flavours of quark, the up quark and the down quark, can combine together in different ways to form protons and neutrons. In other words, protons and neutrons are actually not the smallest building blocks of matter. They are not fundamental particles. And when we say fundamental particle, what we mean is that they cannot be split into smaller particles. And so protons and neutrons are not fundamental particles because they can be split up into quarks.

However interestingly, we still believe electrons to be fundamental particles. As far as we know, we can’t split electrons into even smaller particles. Now, as we said earlier, up and down quarks combine together to form protons and neutrons. There are other kinds of more exotic quark out there. But those do not combine to form protons and neutrons specifically. So for now, we won’t be thinking about those. Let’s instead take a look at just how these up and down quarks combine together to form protons and neutrons.

Let’s start by thinking about a proton. A proton is actually made up of two up quarks and one down quark. And to see how this can make sense, let’s recall that an up quark has a relative charge of positive two-thirds. And a down quark has a relative charge of negative one-third. Hence, the total charge on this particle, which is made up of two up quarks and one down quark, is positive two-thirds from one of the up quarks plus another two-thirds from the other up quark minus one-third from the down quark. And because all of the denominators are exactly the same, we can simply add the numerators in the fraction. What we get is two plus two minus one.

And so as an end result, we have positive three divided by three, or in other words positive one. And we can also recall that a proton has a relative charge of positive one. So that quite literally adds up. Based on the charges on up and down quarks, a proton is made up of two up quarks and one down quark. A neutron on the other hand, which we can recall is a neutral particle and therefore has a relative charge of zero, is made up of two down quarks and one up quark. So let’s see what the total charge on this set of particles is. Well, we can see that the up quark will contribute a positive two-thirds relative charge. And then a down quark will contribute negative one-third. And the other down quark will also contribute negative one-third.

So plus two-thirds minus one-thirds minus one-thirds, actually gives us a relative charge of zero, just as we’d expect. Now, there’re a couple of different things to note here. Firstly, it’s highly likely that up quarks and down quarks have different masses. They’re theorized to have different masses. And experimental results also showed that they have different masses although we don’t yet have very accurate values for these. But then if we said that the up quark has a mass of 𝑚 subscript 𝑢 and a down quark has a mass of 𝑚 subscript 𝑑, then what we’re saying here is that 𝑚 subscript 𝑢 is not equal to 𝑚 subscript 𝑑. And what this means is that a combination of two up quarks and a down quark will have a different mass to a combination of two down quarks and one up quark.

In other words then, the mass of a proton and the mass of a neutron are slightly different. Now, this definitely is the case. We have got high precision experimental values that tell us the masses of protons and neutrons are different to each other, only very slightly. So that we usually ignore this in most of our calculations. But nonetheless, their masses aren’t exactly equal. It turns out that neutrons are actually very slightly heavier than protons. The mass of a proton to three decimal places is about 1.673 times 10 to the power of negative 27 kilograms. However, the mass of a neutron is about 1.675 times 10 to the power of negative 27 kilograms. And this mass difference may be accounted for by the difference in mass between up and down quarks.

The other thing to note is that quarks do not exist on their own. They’re always found in pairs or in threes as we’ve seen here. But isolating a quark is extremely difficult. This is why it was very shocking to us when we first discovered that particles could have fractional charges compared to that of a proton or an electron because it wasn’t common place to observe quarks, whereas it was really easy to observe protons and neutrons. And so we thought that the smallest possible charge there could be on any particle was the charge of a proton or an electron. So now that we’ve learnt a little bit about up and down quarks, let’s take a look at an example question.

The nucleus of a helium-4 atom contains two protons and two neutrons. How many up quarks are in the nucleus in total? How many down quarks are in the nucleus in total?

Okay, so in this question, we’re dealing with a helium-4 atom which we’ve been told consists of two protons and two neutrons. Now, let’s start by recalling that both protons and neutrons are made up of quarks, specifically up and down quarks. A proton is made up of two up quarks and one down quark, whereas a neutron is made up of one up quark and two down quarks. So based on this information, we can see that our helium-4 nucleus is made up of two protons, each of which contains two up quarks and a down quark, and two neutrons, each of which contains two down quarks and one up quark.

And now, all we have to do is to add up the number of up quarks in this nucleus and down quarks in this nucleus too. So let’s start with up quarks. Let’s say that the number of up quarks is equal to the number of up quarks in a proton, which is two, multiplied by the number of protons in the nucleus, which is two. And then to this we need to add the number of up quarks in the neutrons. So each neutron contains one up quark. And there are two neutrons in the nucleus, one, two. And at that point, we’ve accounted for all of the up quarks in the nucleus. So we just need to simplify the right-hand side of this equation. We can, therefore, see that the total number of up quarks in this nucleus is six. And we can confirm that by actually counting them, one, two, three, four, five, and six. And hence, our answer to the first part of the question is that there are six up quarks in the nucleus in total.

Moving on to the number of down quarks in this nucleus then, we can say that this is equal to, firstly, the number of down quarks in protons where each proton has one down quark in it and there are two protons in the nucleus. And to this we need to add the number of down quarks in the neutrons. Now each neutron has two down quarks. And there are two neutrons in the nucleus. And so when we evaluate the right-hand side of this equation, we find that there are also six down quarks in this nucleus. Let’s confirm that by counting, one, two, three, four, five, and six. Hence, our answer to the second part of the question is that there are six down quarks in the nucleus in total.

So now, that we’ve answered that question, let’s take a look at another example.

The table shows the relative charges of the up and down quarks. If a composite particle were made up of three up quarks, what would the relative charge of that composite particle be?

Okay, so in this table, we can see that there are the up quark and down quark given in the table as well as their relative charges. The up quark has a relative charge of two-thirds. And the down quark has a relative charge of negative one-third, where, of course, relative charges are measured relative to the charge of a proton. In other words, an up quark has a charge that is the same sign as the charge on a proton, it’s positive. But the magnitude or size of that charge is only two-thirds the size of the charge on a proton. And in the same way, the down quark has a negative charge. So the sign of the charge is opposite to that of the proton. But the magnitude or size of that charge is one-third that the magnitude of the charge on a proton.

Now, we’ve been told that a composite particle is made up of three up quarks. So here they are. One, two, three. And as we know, each up quark has a relative charge of positive two-thirds. So the total charge on this composite particle is going to be positive two-thirds from one of the up quarks plus another two-thirds from the second up quark plus a final two-thirds from the third up quark. So this becomes two-thirds plus two-thirds plus two-thirds which simplifies to positive six divided by three. And that is the same thing as positive two. And hence, we can say that the total relative charge on a composite particle made up of three up quarks is positive two.

Okay, so now that we’ve had a look at a couple of example questions, let’s summarise what we’ve talked about in this lesson. We, firstly, saw that protons and neutrons are made up of fundamental particles known as quarks. Now, fundamental particles are particles that cannot be broken down any further. Another example of a fundamental particle is an electron. Coming back to protons and neutrons, we saw that this is specifically made up of up quarks and down quarks. We saw that up quarks have a relative charge of positive two-thirds. And down quarks have a relative charge of negative one-thirds, where these relative charges are measured relative to the charge on a proton.

Lastly, we saw that protons are made up of two up quarks and one down quark, whereas neutrons are made up of one up quark and two down quarks. And the fact that these up quarks and down quarks may have different masses to each other can be used to explain why protons and neutrons have different masses to each other. So this is how up and down quarks from the basic building blocks of the most common types of matter in our universe.