Which of the following particles are hadrons?

04:25

### Video Transcript

Which of the following particles are hadrons? mu neutrino, lambda baryon, charm quark, top antiquark, pion, proton, electron.

To figure out which of these particles are and are not hadrons, let’s first recall what this term means. A hadron is a composite particle made up of two or more quarks with a total relative charge equal to some integer value. To understand hadrons then, we need to understand quarks and their antiparticles, antiquarks. The six types of quark are up and down, charm and strange, and top and bottom, where the three quarks in the top row of this grid have a relative electric charge of positive two-thirds times the charge of a single proton, while those in the bottom row have a relative charge of negative one-third e, while each corresponding antiquark has a charge of the same magnitude, but the opposite sign.

Hadrons then are made up of these six types of quarks and their antiparticles. And so, the first test we can apply to these particles to see if they’re hadrons is to determine whether they’re made up of two or more quarks or not. Starting at the top of our list, our first particle is called a mu neutrino. This is a fundamental particle. That is, it’s not made up of any smaller particles as far as we know, and, therefore, it doesn’t meet the condition of being made up of two or more quarks, as all hadrons are. This shows us that a mu neutrino is not a hadron, so we’ll cross off that option.

Next, we come to the lambda baryon. This is a particle that is made of quarks. And in fact, the three quarks that it’s comprised of are given to us. If we bring together an up, a down, and a strange quark, then we have what’s called a lambda baryon. So this particle is made of two or more quarks. And now we just need to know whether its total relative charge is equal to an integer. To figure that out, we’ll add together the relative electric charge of each of these three quarks. Based on our grid of quarks and antiquarks, an up quark has a relative electric charge of positive two-thirds, and we’ll leave off the e.

A down quark, on the other hand, has a relative electric charge of negative one-third, and so, we see, does a strange quark. If we add all these up, we get a result of zero. Now zero is an integer value, and so that means it satisfies the second condition of a hadron. Therefore, a lambda baryon is a hadron, and we’ll box in this particle as part of our answer. Moving on, we come to the charm quark. Just as a side note, if we saw this without any context, we might think that this c refers to the speed of light in vacuum. The only way we really know that this refers to a charm quark is because we’re told that it is a particle. And therefore, we identify it with this particular quark type.

As we’ve seen, a hadron is a composite particle made up of two or more quarks. So one quark all by itself can never make a hadron. The charm quark, then, is not a hadron. Moving down to the top antiquark, for the same reason, this also is not a hadron. A hadron needs to have at least two quarks. This brings us to the pion which we’re shown is comprised of an up quark and a down antiquark. If we draw that out, it looks like this. And so this particle is made up of two or more quarks. In particular, it’s made of two. So once again, we need to test whether its total relative charge is equal to an integer. The relative charge of an up quark is positive two-thirds and that of a down antiquark we see is positive one-third. This adds up to one, which is an integer, which means that this particle, called a pion, is indeed a hadron.

We’ll box that particle then and move on to consider the proton. A proton is made up of two up quarks and one down quark. That would look like this. And once again, we’ll look at the total charge for this particle. Each of the up quarks contributes a relative charge of positive two-thirds, while the down quark, negative one-third. And this adds up to three-thirds or simply one. Just like we would expect, the total charge for this proton is positive one. And since that’s an integer, it means that a proton is a hadron.

The last particle we’re to consider is an electron. Like a mu neutrino, an electron is an elementary or fundamental particle. It’s not made of anything smaller than itself, so it’s not made up of two or more quarks. This tells us that an electron is not a hadron. So of this list of particles, the lambda baryon, the pion, and the proton are hadrons.