Thanks to Google for sponsoring a portion of
this video, for supporting small businesses, and for helping people find
jobs. More about 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 particles?
Is the electron inside it? Or on the surface? Why do some of them have more 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 orbiting? How much energy does it have?
How big is the 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 wavefunction 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 3D, here’s what you get. Isn’t it beautiful? Here’s 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 love it. You can see the patterns in the orbitals, you can get a sense that they actually
ARE orbitals (I mean, something is orbiting!). Ok, so I do have to be clear: the dots don’t
each represent a separate electron - the whole collection represents the wavefunction 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). Electrons with more
energy are more likely to be far away from the nucleus, so higher energy orbitals are bigger.
The motion of the dots is showing the “flow” of the wavefunction, 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 wavefunctions 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 too. 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 three
“P” orbitals (the ones 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 points
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,
if one is oriented spin up and one spin down. THIS is a MinutePhysics-approved
cartoon representation of an atom. Thanks to Google for sponsoring this portion
of my 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 equations, 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. Ok, the sponsored segment is
over and you're still here! You probably want to know about the
rainbow donuts. The color there represents the "phase" of the wavefunction, which informs
how different wavefunctions interfere with each other, and it's essentially being
represented by motion in my 3D visuals.