In a two-dimensional version of our universe, electrons would still orbit atoms and there would still be a periodic table for the elements, but it would be different from our table and would look like this.

Here is why.

This is oversimplifying, but the chemical properties of an atom are determined by how its outermost electrons are behaving, since they are the most weakly attracted to the nucleus and therefore most available to interact with other atoms.

So, roughly speaking, the periodic table is a diagram of which orbital happens to be the outermost one for each atom.

In 3D, the possible orbitals of an electron have energies that look something like this, left to right means orbiting with more angular momentum, and bottom to top means orbiting with more energy and generally more distance.

When you throw a bunch of electrons around a nucleus, they fill up the possible orbitals and don't share them more than two per orbital because electrons don't like each other.

Kind of like water filling up a funny shaped tank.

So, which orbital the outermost electron is in depends on both the shape of the tank and how full you fill it, that is how many electrons there are.

Technically speaking, each electron you add changes the shape of the tank, so what we're showing here is actually something more like the level of each orbital if it were the outermost one, not the actual levels.

Also, we don't have a good explanation for why the tank has the shape it does, but that's a topic for another video.

When you gradually fill up the tank to see what the outermost orbital of each element is, you get our periodic table, well, after a slight rearrangement.

For 2D atoms, there are two big differences.

First, while in 3D the electromagnetic force that attracts electrons to the nucleus is a one over r squared law, since it depends on the surface area of a sphere, in 2D, a sphere is just a circle whose surface area is its circumference, so the electromagnetic force is a one over r law.

This difference changes the vertical spacings, the energy levels.

And second, because in 2D there are fewer dimensions in which to move, there are also fewer ways for electrons to orbit, which means fewer orbits for each energy level.

In particular, for a given amount of angular momentum, an electron can only be orbiting clockwise or counterclockwise, unlike 3D where there are a lot more possible orientations.

So, for each value of angular momentum, there are only two possible orbitals at each energy level.

If we gradually fill up the 2D orbitals with electrons to see what the outermost orbit of each element is, the result is a table that looks like this, or after a slight rearrangement, something more like the typical table for our 3D universe.

But it's definitely different.

There are two ways we might name the 2D elements.

We could use the same names as the 3D ones with the same number of protons and electrons.

So that carbon, sulfur, zinc, and cadmium would be the names of the 2D noble gases, and the 2D halogens, which in 3D are fluorine, chlorine, etc, would be instead boron, phosphorus, copper, silver, etc.

The other proposal is to name 2D elements based on the equivalent chemical properties.

So that the noble gases are still neon, argon, krypton, etc, the halogens are still fluorine and chlorine, and so on.

This second naming proposal means we leave out a lot of names, but we also get to add some new ones because there are blocks in the 2D periodic table that we don't have in the 3D one.

So, what's the point of a 2D periodic table?

I mean, maybe it could help predict the behaviors of quasi particles on a 2D surface like a thin layer of graphene.

Maybe it can help improve mathematical techniques.

But mostly, I think it's an exercise in curiosity, it's simply cool that we can calculate and predict the whole 2D periodic table and have confidence that it's reasonably accurate since the same type of calculations correctly predict the 3D table, even if we could never actually experience a 2D universe.

What's not.

There are two other issues that might totally invalidate this table, but I'll get to those in a minute.

This video was supported in part by Nova PBS's new documentary, Decoding the Universe, Quantum.

You can stream it right now on Nova's YouTube channel, which is linked in the description.

We need to know how things interact on a fundamental level, entanglement is the stubborn, disturbing, interesting and the most confusing.

Part of what it means to describe how nature works.

Decoding the universe, quantum.

Stream now.

Go to the link in the description to watch Nova's Decoding the Universe, Quantum.

And thanks to Nova for their support of Minute Physics.

Okay, so the two issues that could completely invalidate the rest of this video.

One, I have not looked at all into whether 2D nuclear physics allows stable nuclei, although it seems reasonable.

If you don't have a nucleus, you can't have an atom.

And two, because of the nature of the electromagnetic force in two dimensions, it's not actually possible to ionize an atom, that is to remove an electron completely, so molecules and chemistry might be totally different and very weird and the periodic table might be irrelevant.

If you'd like a drawing from this video or any other Minute Physics video, go to patreon.com/minutephysics right now, I'm giving away all my drawings.