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Maroon5 has it right, in a way. The ones right below the level of the atom are pretty much protons and neutrons in the nucleus, and electroncs orbitting in electron clouds. However, there is so much more depth here, and so many more than 3 subatomic particles.
For example, protons and neutrons are made up of up and down quarks (up-up-down = proton, up-down-down = neutron, in both cases one of each color must be present), and electrons have no known substructure.
So, you may be able to say "up quarks, down quarks, and electrons," as your answer to be a little more correct!
Wait! But, how does that nucleus stay together? The forces holding the nucleus are pretty strong, and are labelled, appropriately, the Strong force. What transmits the strong force? Particles called gluons do! In fact, we have 8 of them! Well, there go our limit of 3 subatomic particles...
However, now, we start thinking about other things. What if "subatomic" doesn't mean "the stuff inside an atom." What if it means "not as big as an atom"? Well, then we start upon a long, long journey of particle physics that isn't even complete (have you heard of the Higg's Boson? yeah, if they find that, we'll be good, otherwise, we're going to have to throw a lot of things out).
So currently known subatomic particles are a LOT more than 3. In fact, everything in physics now is looked at as both a particle and wave. So a photon could be seen as a subatomic particle. There are 4 more types ("flavors") of quarks and 3 "colors" for each quark! There are leptons, bosons, muons, tau particles, the list goes on.
So what are the 3 atomic particles? First, there are certainly more than 3. Second, you can't name them all, because we don't even know if we've found them all!
I hope that helps, but granted, it is a bit confusing. However, you're in good company. Richard Feynman, who got the Nobel Prize with some other people for quantum electrodynamics, said at one point, "It is safe to say that noone understands quantum mechanics." But hey, if you read the link below and can conceptually differentiate between a boson and a lepton, I think your teacher will be required to give you an A. Just kidding, but maybe!
1)Protons - positivily charged
2)Electrons - negativily charged
3)Neutrons - no charge
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