We're taught in science class that atoms listed on the periodic table consist of a ball called a nucleus surrounded by a bunch of electrons. Let's talk about electrons and how we can identify each and every one of them.

Every electron in an atom has a series of numbers that uniquely identifies it much like a street address defines your home. These numbers are called quantum numbers. Each number is associated with a particular GEOMETRIC PROPERTY. These geometric properties define regions of space in an atom in which each electron might be found. These regions are called orbitals -- for lack of a better word since electrons don't exactly orbit but jitter about within their orbitals. They collectively form a sort of electron cloud. Well, even that's not quite right, but let's keep things simple for this tutorial. Back to geometry . . .

If there's only one electron in an atom like hydrogen, it's a simple one-dimensional problem. To describe this, we only need one quantum number. It's called the principal quantum number, n. The geometric property associated with n is the SIZE of the orbital. It has to do with how far away the electron might be found from the nucleus.

Since there are more electrons in other atoms, we need three spatial dimensions and two more quantum numbers. These are called the angular and magnetic quantum numbers, labeled, l and m, respectively. The angular quantum number is determined by the geometric property of the orbital's SHAPE. The magnetic quantum number is determined by the geometric property of the orbital's ORIENTATION. It's all geometry!

A useful illustration of these geometric properties is a dumbbell-shaped orbital (see picture). It has a particular size, shape, & orientation. We label these geometric properties n, l, and m. Each label is an integer value like 1, 2, 3, and so on.

Finally, every orbital represents up to two electrons. That is to say, the dumbbell-shaped orbital may represent a different electron in each of its lobes -- say the upper or lower lobe. So, we need another number to represent each electron's geometric property of LOCATION within the orbital. This is the spin quantum number, s. This number is either +1/2 or -1/2 depending on which lobe of the orbital an electron might be found.

Now, we could get into how these geometric properties give rise to a variety of physical quantities like energy, angular momentum, and so on. We could also get into some physics concepts like Pauli's Exclusion Principle, but let's leave it here for today with this rudimentary tutorial about geometric properties of quantum numbers in the periodic table.

Maybe expanding on the street address analogy is useful. Think about how every electron CAN have a roommate. Think about how some houses are empty; others are not. Just don't stray too far from geometry. Let this tutorial settle in. Give it some thought. Einstein thought a lot about geometry. So should you.