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.