A Better Way To Picture Atoms

Thanks to Google for sponsoring a portion of this video, for supporting small businesses, and for helping people find jobs. More about all that at the end. Atomic orbitals have long been a source of frustration for me. On the one hand, you have simple cartoon diagrams that make them feel friendly, but which are so varied and vague they don't really convey much beyond the basic idea that atoms have a nucleus and some electrons. Some people try to take the cartoony diagrams and make them feel more random or quantum, which is an improvement, but they're still very much just cartoon stand-ins for the vague idea of atom. On the other hand, you have atomic orbitals depicted as fuzzy clouds or balloons or rainbow donuts, which are definitely more technically accurate or technically inspired, but none of which feel like they give me a sense of what's actually going on. Like, what does this blobby thing have to do with orbiting electrons? Is the electron inside it or on the surface? Why do some of them have blobs and others donuts? And why are some of the donuts rainbow-colored? I want to know what an atom looks like, and I want that picture to actually have something to do with the nitty gritty reality of atoms, since they are indeed real things. You know, like how a diagram of the solar system is both a totally not-to-scale caricature, and yet also represents the very real idea that the planets all orbit the sun in roughly the same plane, and that some are farther out and some are closer in, and if it's animated we get to see that the closer planets complete their orbits more often? It's a nice picture, and that's what I want for atoms. A good picture. There are a few things I'd like that picture to get across, some of them because they're important for the physics of atoms, and some of them because they're questions my brain wants answers to. Like, where is the electron? How fast is it going? How much energy does it have? How big is this picture relative to other pictures? Of course, the wave-particle nature of quantum mechanics means some of these ideas, like the electron's position, don't translate exactly from our everyday intuition to the atomic scale. But there is a way of thinking about wave-particle duality where you picture the wave function as a bunch of water, and the particle as a speck of dust in that water. The particle is mostly guided by where the water goes, and the water is guided by the equations that determine how water behaves depending on its circumstances. And if you apply the mathematics of that idea to atomic orbitals, and then render it in three dimensions, here's what you get. Isn't it beautiful? Here's another. And another. And another. In fact, I made a bunch of these, and they're all mesmerizing and beautiful, and isn't the ground state of the hydrogen atom just so cute? And aren't the excited states so majestic? There's so much structure and detail in them, I just love it. You can see patterns in the orbitals, and you can get a sense that Okay, so I do have to be clear. The dots don't each represent a separate electron. The whole collection represents the wave function of a single electron, and the individual dots represent all the places that electron could be. A higher density of dots means a higher probability of the electron being there. The bigger orbitals are the ones with higher energies, because electrons with more energy are more likely to be far away from the nucleus. The motion of the dots is showing the flow of the wave function, and does correspond to an extent with its actual angular momentum, though they're not electron trajectories. Unless you think Bohmian trajectories are real, in which case they really are electron trajectories. I'll let the philosophers of physics fight that one out. But the point is, these visuals are created by representing actual electron wave functions in a visual language that our brains can understand, that of objects and light and shadows and motion in 3D space. There's actually stuff orbiting. And they're pretty. I hope you like them as much as I do. Oh, one final thing. I 100% get that these are not easy to draw. So if you want a cartoon representation of an atom that's simple but more closely based in atomic physics, here's my proposal. It's based on the orbitals from the p-block of the periodic table. One of them has the electron orbiting one way, one in the opposite way, and in the third one the electron is orbiting the same amount, but around some perpendicular direction, and we can't know which. Which is why the dots aren't moving in the middle orbital, and why I've drawn a dotted line and question mark for the sideways circle. And if you want, you can add an electron to each orbital, or two electrons, one oriented spin up and one spin down. This is a MinutePhysics-approved cartoon representation of an atom. But really, the beautiful 3D ones are where my heart is. Thanks to Google for sponsoring this portion of the video. When Google reached out to sponsor MinutePhysics, I immediately said yes, because I use Google search literally every day for everything from 3D software tutorials to physics questions, the weather, recipes, and of course coronavirus vaccine information. And Google has been focusing a lot on supporting individuals and small businesses over the last year. Google can even help you or your family and friends discover opportunities and find jobs where you live. Just search jobs for physics majors, or jobs for veterans in Montana, or jobs for whatever it is you do, and Google will help you find opportunities tailored to you. Thanks again to Google for sponsoring this part of my video, for making it easy to convert centimeters to inches, and for helping us all find the information we need. Okay, the sponsored segment is over and you're still here, so you probably want to know about the rainbow donuts. The color there represents the phase of the wave function, which isn't directly measurable, but which informs how different wave functions interfere with each other, and it gets more or less represented by the motion in the 3D visuals.