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In a two dimensional version of our universe, electrons would still orbit atoms and there would still be a periodic table for elements, but it would be different from our table and would look like this. Let's explore why. This is oversimplifying, but the chemical properties of an atom are determined by how its outermost electrons are behaving, since they're 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.
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 1/r2 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 1/r law; this difference changes the vertical spacings of 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,
which looks like fewer horizontal spaces in the energy levels. 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. Except for the lone zero angular momentum orbital, which isn't going clockwise or counterclockwise. If we gradually fill up the "tank" of 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! Is a 2D periodic table useful? I don't know. Maybe it could help predict the behaviors of quasiparticles 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. And any differences and similarities we find can help show us/help us see what's unique about the 3D periodic table and what's not.
