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.