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One of the surprises of modern science was that atoms and sub-atomic particles do not behave like anything we see in the everyday world. They are not small balls that bounce around. These particles can only be described as abstract objects that interact mathematically and behave in ways that make no intuitive sense to our normal understanding of matter.
Physicists use the word "quantum," which means "broken into increments or parcels," to describe the physics of very small particles. This is because certain properties are only found in discrete units. For example, you can only find integer electric charges (...-1, 0, +1...). Quantum mechanics describes particle interactions.
A few of the important quantum particle properties are:
Electric charge. Quarks may have +2/3 or -1/3 electric charge, but they form composite particles with integer electric charge. All other particles have integer electric charge.
Color charge. A quark carries one of three color charges and a hadron carries of one eight color-anticolor charges. All other particles are color-neutral.
Flavor (for quarks) or lepton number (for leptons). Flavor distinguishes quarks from one another, and lepton number distinguishes leptons from one another.
Spin. Spin is a bizarre but important physical quantity. Large objects like planets have angular momentum and a magnetic field because they spin; since particles also appear have their own angular momentum and tiny magnetic fields, physicists called this particle property spin. This is a misleading term since particles are not actually "spinning." Spin is quantized to units of 0, 1/2, 1, 1 1/2, and so on.
Mass may also be a quantum property, but the Standard Model does not yet describe how particles get their masses.