Hey Crazies.
You’ve probably seen atomic orbitals before.
They’re those weird-looking shapes that show up near the end of a chemistry class.
The problem is they’re always so static.
The universe isn’t static. It’s dynamic. It’s all about change.
Atomic orbitals are no exception.
Let me show you the way they were meant be seen.
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Our first obstacle is going to be that we can’t actually see any of this,
at least not directly.
The super tiny wavelengths of visible light are thousands of times larger than an atom.
Optical images just aren’t possible at that scale.
The best we can do is a diagram based on electron microscope data.
Every one of these spherical lumps is a gold atom.
That makes atoms look like tangible little balls, which they aren’t
and it doesn’t tell us much about what’s happening inside.
I mean, with such a simple image, there could be cake in there.
Spoiler Alert: It’s not cake.
The cake is a lie.
I think it’s common knowledge at this point that atoms are made of three things:
Protons, Neutrons, and Electrons.
They’re called sub-atomic particles, for obvious reasons.
Based on experiment, we know the heavy protons and neutrons are packed into a tiny nucleus
and the electrons fill a volume a hundred thousand times larger.
The complete collection is what we call an atom.
Since electrons fill the vast majority of the volume of their atom,
they tend to control what their atom does.
This makes understanding their behavior extremely important.
But figuring that out was a pretty difficult process, historically speaking.
To the timeline!
We went from floating in a mist, to orbits, to circular standing waves,
all of which were ruled out by experiments.
By 1926, we were left with only one option: Quantum Mechanics.
Which, as many of you know, borders on absurdity.
Quantum mechanics is weird, y’all, and you can quote me on that.
And, if we’re wrong about it,
the universe can only be weirder than we already think it is.
Remember, we ruled out all the normal stuff.
Is this where atomic orbitals come in?
Yep! Let me make something absolutely clear though.
Electron orbitals are not orbits, like at all.
Like any quantum state, an orbital is a state of probability.
Yes. Really.
Here’s an example of an orbital.
Brighter spots are where we’re more likely to find an electron
and darker spots are where we’re less likely to find one.
But the truth is we don’t actually care that much about where electrons are.
Position is a pretty pointless property.
What do we actually care about then?
Energy and angular momentum.
You know, conserved properties.
In fact, Schrodinger’s equation is an energy equation.
[Panicked Look]
Don’t freak out. I’m not going through a full derivation or anything.
If you want to see that, you'll find it in excruciating detail in my book.
But quantum mechanics is, like, 90% math.
If want to learn more than just the buzz words,
you’re going to have to deal with at least a little math.
Get on board.
Anyway, this is just kinetic energy plus potential energy equals total energy.
That’s it. That’s all this is.
A quantum version of the conservation of energy.
Half the battle when using this equation is figuring out what the potential energy is.
In our case, it’s what holds the electrons in the atom
and its influence is entirely radial.
You can actually see that pretty clearly in the electron microscope image from earlier.
That’s why these look like tiny spheres, because their influence is radial.
To take advantage of this behavior, we’ll need one of my favorite tools:
spherical coordinates.
They’re so cool!
[off camera] NERD!
Oh shush.
Rather than three linear labels like x, y, and z;
we use a distance from the center,
an angle from the vertical,
and an angle around the horizontal.
Since the potential energy only depends on the distance from the center,
it can be separated in our solution to Schrodinger’s equation.
It gives us an idea of size where the angle part gives us an idea of shape.
Let’s focus on the shapes first.
They’re called the spherical harmonics.
Notice how they’re all oriented along the same axis.
One angle draws a curve and then the other angle makes it a surface.
Each one of these shapes goes with a specific angular momentum.
It’s what we call orbital angular momentum
because these are orbitals, not orbits.
The axis they’re lined up with is the direction we’re measuring the momentum along.
Because this is quantum mechanics, we're only allowed to measure along one axis at a time.
That’s kind of limited, isn’t it?
Yeah, but it’s actually enough.
One number tells us how long this angular momentum arrow is.
The other number tells us its orientation
by projecting the arrow onto the measurement axis.
These two numbers are all you need to know the shape of the orbital.
You can even organize them into a nifty chart like this.
Man, I love charts.
I mean, look at this thing.
Mmmm yisss!
Unfortunately, none of those shapes are probability distributions yet
because we left out the radial part.
It’s only half the solution.
Including the radial part, turns our shapes into probabilities.
It turns these into these,
which are further organized by energy level.
These are just probability distributions.
Brighter spots are where we’re more likely to find an electron.
Darker spots are where we’re less likely to find one.
It’s a visual of where you might find something, if you looked.
We generally don’t look though because we want the position to be uncertain.
That way the energy and angular momentum remain definite for each state.
But, like I said at the beginning of the video, this all looks pretty static.
Atomic orbitals are actually dynamic.
An electron can absorb or release photons, which can change that electron’s energy.
Electrons can jump between quantum states.
Based on what I’ve mentioned so far, you’re probably only imagining a simple fade.
But it’s actually cooler than that.
Quantum mechanics might be weird, but it’s still a set of rules.
The events might be probabilistic, but the probabilities are deterministic.
And that probability must be conserved, just like energy and momentum.
That means you can imagine the probability as if it’s a fluid filling all of space.
When the distribution changes, that probability has to flow to the new locations.
Orbital transitions look more like this.
That flow is called a probability current.
Kind of cool, huh?
So what’s an atomic orbital?
A quantum state of probability.
The angular momentum tells us the shape.
The energy fills the volume of that shape with detail and gives us an idea of size.
Brighter spots are where we’re more likely to find an electron.
Darker spots are where we’re less likely to find one.
But the probability of finding it somewhere must be 100% at all times.
Quantum probability is conserved.
When an electron changes quantum states,
that probability has to flow to the new locations in a kind of probability current.
So on some level, maybe the cake isn’t actually lie after all.
As long as, by cake we mean probability.
So, what do you think? Is the cake a lie?
Let us know how you feel in the comments.
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And until next time, remember, it’s ok to be a little crazy.
Could an AI be alive?
Well, it could eventually become self-aware, at which point we should respect it as a conscious being.
But that doesn’t necessarily make it alive.
Consciousness and life are two totally different things.
Anyway, thanks for watching.