Every electron in every atom has a type of address, called its quantum numbers. If you look at this model of zinc atom, each colored region represents a region where one or two electrons are most likely to exist. By understanding the quantum numbers that define a given electron, we can better understand how both atoms and electrons behave. Let's look at these quantum numbers.

There are four quantum numbers. The first is called the principal quantum number, which we shorten to “n.” The second is the angular quantum number, which we abbreviate as “ℓ,” usually written in cursive, so it doesn't look like a 1. The third quantum number is the magnetic quantum number, or “m-sub-ℓ.” And the fourth is the spin quantum number, or “m-sub-s.” Let's look at each of these numbers in greater detail.

The first is the principal quantum number, n. We sometimes call this the “shell” or the “energy level.” And it indicates, on average, how far away the electron is from the nucleus in a given orbital. The principal quantum number is limited to positive integer values, for example 1, 2, 3, up to about 7. Anything beyond 7 is mostly theoretical.

The second quantum number is the angular quantum number, or ℓ, and this indicates the shape of the orbital. As you can see there, when l is equal to 0, it's a sphere, which we call an s orbital. When ℓ is qual to 1, it's a dumbbell, which we call a p orbital, and so on with d and f orbitals. The lowest possible value for ℓ, the angular quantum number, is 0, corresponding to the sphere shape. And the highest possible value is n minus 1, where n is the principal quantum number. So if you have a principal quantum number of n equals 3, then you can have angular quantum numbers of 0, 1, or 2.

The next quantum number is called the magnetic quantum number, or m-sub-ℓ. The magnetic quantum number tells us the orientation of an orbital around the nucleus, and it's limited to integers ranging from negative-ℓ to positive-ℓ. So when ℓ equals 0, there's only one possible value for m-sub-ℓ: zero. And that makes sense, because there's only one possible orientation of a sphere. You can rotate that sphere however you like, it's going to look the exact same. By contrast though, when ℓ equals 1, which is the dumbbell shape, there are three possible orientations, which are lining up to the x-axis, y-axis, and z- axis. Three orientations for the three possible m-sub-ℓ values: negative 1, 0, and positive 1. So when ℓ equals 2, there are five possible orientations, and when ℓ equals 3, there are seven possible orientations.

The last quantum number is the spin quantum number, and this quantifies the angular momentum of the electron. Now, it's worth noting that the electrons are not actually physically spinning like a top. This is just quantifying a certain attribute that electrons exhibit. And there are only two possible values for the spin of an electron: positive one half or negative one half. Which, when we're writing this down, we usually denote positive one half with an upward arrow, and negative one half with a downward arrow.

Using these four quantum numbers, we can define any given electron within an atom. And by understanding these four quantum numbers, we can better understand how electrons interact with the atoms that they are a part of, and indeed, how chemical reactions occur.