 So we understand now that energies are quantized, both the energies of things like light, which has a certain discrete number of quantum mechanical particles or photons, and also the energy levels of matter, atoms and molecules, are also quantized. But it turns out, not only the energies are quantized, but also the states that matter can exist in are also quantized. I guess let me point out right now, when I say states of matter, that might immediately bring to mind states of matter like solid, liquid, gas. Many textbooks might use the word state of matter to describe solids or liquids or gases. We'll use the word phases of matter to describe different physical phases like solid or liquid or gas. When I say states of matter, I mean the same thing as when I say the states that have a certain energy of a molecule like the ghost or the anti-state of butane, I'm just talking about the arrangement of the molecules in some way that describe the system. So states of matter doesn't have anything to do with solids or liquids or gases. So it's already a little bit weird, depending on how used to this fact, the quantum mechanical fact you are, that the energy levels of matter are quantized. The fact that a particular molecule or a particular system can have energy E sub one or energy E sub two, but it can never have, if I want the molecule to have this much energy, I just can't do it. It can never have that much energy. It only has these specific discrete quantized amounts of energy. So that's already a little bit weird, but what's even weirder is the fact that the arrangement of the particles in the matter itself are quantized, meaning they can only exist in certain ways as well. That's definitely not the way we're used to thinking of macroscopic objects behaving, let's say this marker. I imagine that I can make this marker take on any orientation I want, but at the microscopic level that's not true. If I start talking about small things like electrons and atoms and molecules, turns out I can make them take on certain arrangements and I can't make them take on other arrangements and that definitely begins to feel a little bit weird. But to show us that you already know something about this as an example and as evidence for why we know this is true about at least small quantum mechanical objects, we'll go back to the example of the hydrogen atom in particular. Continue thinking about the orbitals in a hydrogen atom. So we know that the electron in the hydrogen atom can be in the 1s or the 2s or the 2p or the 3s, 3p, 3d and so on orbitals. There's a lot of different orbitals that the electron can occupy. Those orbitals if we were to draw them, so an s orbital we know has spherical symmetry. So the electron is delocalized or spread out in this spherical electron cloud that differs from let's say a p orbital which has a dumbbell shape. And again the electron is spread out or delocalized in this dumbbell shaped electron cloud. There's a large number of different orbitals which have their own shapes. A d orbital is a clover leaf type shape. F orbitals have eight lobes instead of four and so on. So there's many, many different shapes the electron can have. But notice that there's shapes that don't fall in this collection of different orbitals. For example, so these shapes, the ones I've drawn, these are all perfectly fine. These are allowed states of matter. These are allowed configurations that the electron in the hydrogen atom is allowed to have. There's other states that are not allowed. I cannot make the electron in a hydrogen atom let's say take on that shape. Even if I delocalize the electron I spread it out around this heart shape. That's just not a shape that an electron takes on in a hydrogen atom in the real world. There are no heart shaped electrons no matter how many different orbitals that continue out in this pattern. You're not going to find one that is a heart shaped electron. You're not going to find one that's a diamond shaped orbital for an electron and so on. So you're familiar with the fact even though now that you're thinking about it it might seem a little strange. Certain shapes of the electrons are allowed. Certain shapes you've never seen them and that's because they're not allowed. Nature doesn't allow those to exist. So it's not just the energy levels that are quantized. In fact the reason the energy levels are quantized is because the physical arrangement of the electron itself is quantized. Only certain discrete shapes or orientations or arrangements will have other words to describe this behavior of the electron. Only certain arrangements of the electron in a hydrogen atom are allowed. Each one of those corresponds with one of these different energies. So discrete quantized energies exist because the electron itself can only exist in certain patterns as well. And perhaps if I were able to make a heart shaped electron it would have some other energy but it would be one of these disallowed energies. So that's one of the other weird features of quantum mechanics is it forces matter like electrons and atoms and molecules to take on only certain arrangements. And next we'll conclude our tour of the weird, at least preview anyway, of the weird properties of quantum mechanics by talking about how matter also acts a little bit like a wave as well as like a particle.