The diagram shows a hadron made up of three quarks. What is the relative charge of the hadron?
The two words in this question statement that may be most unfamiliar are the words hadron and quark. Let’s talk for a bit about what those are. We’ll start with the second term: a quark. A quark is a subatomic particle, so it’s like a proton or a neutron or an electron, that carries a fractional electric charge. What that means is that the overall charge of a quark is not some multiple of the charge of an electron or a proton; it’s different. And in fact, there are two different kinds of fractional charge that a quark can have. Though the term quark maybe unfamiliar, these subatomic particles are related to things that we do know a bit better. Protons and neutrons which group together to form atomic nuclei are themselves each made of quarks. We could think of quarks even as building blocks for protons and neutrons.
Now that we know a bit about what a quark is, let’s consider the second term: hadron. We can say that a hadron is a particle with two or more quarks that participates in the strong nuclear force. Remember that the strong nuclear force is one of the four fundamental forces, and it’s responsible for the fact that nuclei of atoms hold together — that is, that the quarks that make up the protons and neutrons hold together — and also for the fact that the nucleus, which according to electrostatics would repel itself since it has an overall positive charge, is able to hold together. We’re told moreover that we have a diagram of a hadron that’s made up of three quarks: one, two, three. We notice that one of these quarks is identified with the letter d and the other two are identified with the letter c. It turns out that these letters refer to particular types or flavors of quark, of which there are six. Here we have a table of quark type also called quark flavor and the particular charge in terms of the charge of an electron that that type or flavor has.
So for example, we see that an up quark has a charge of two-thirds times the charge of an electron, while the down quark has a charge of negative one-third times the charge of an electron, and so forth and so on down through charm, strange, top, and bottom. We bring up these six different flavors of quark because our hadron is made up of more than one type. Notice that one of the quarks in our hadron is abbreviated with d. That tells us that this is a down flavor quark. And the other two are marked out with the letter c, which consulting our table corresponds with the charm flavor of quark. We want to know what is the relative charge of this hadron; that is, a subatomic particle which is made up of these three particular quarks.
To figure that out we’ll work with the corresponding charge of each one of the quarks that’s in this hadron. If we call the relative charge of the hadron capital 𝑄, then we know this will equal one times the charge of a down quark plus two times the charge of a charm quark. Consulting our table, we see that the charge of a down quark is negative one-third 𝑒 or simply negative one-third, leaving our answer in terms of the charge of an electron, and that the charge of a charm quark is positive two-thirds 𝑒 or simply two-thirds. When we combine these results together, we get negative one-third plus four-thirds or positive one. This then is the relative charge of the hadron shown in our diagram.