- I really wanted to make a video about Brownian motion,
this jiggling motion you can see under a microscope, because Brownian motion
does something incredible. It creates a bridge between two worlds, the atomic world and
the macro scale world. And in that in-between world, none other than Albert Einstein was able to do something amazing. In this video, I'm going to show you a few different ways you
can see Brownian motion. I'm going to explain Brownian motion with this model that I made. And finally, I'm going
to show how Einstein was able to work out how much atom's weigh by observing and
measuring Brownian motion. So the first thing I did
was buy this smoke cell kit. You find a way to blow smoke
into this little chamber. It's got this clever light and lens set up to illuminate the smoke
just like dust in a sunbeam. The whole assembly fits
under a microscope. And look, I've got this adapter on mine that I can mount my camera to. This particular method looks
great to the human eye, but for a camera, there's
just not much light. So like I've turned the iso right up here, and you can see there's a decent amount of grain in the footage,
but there you have it. That's Brownian motion. You see that jiggle of
the smoke particles. Robert Brown wasn't the first
person to notice the jiggle, but he was the first person to bring it to wide
attention, hence the name. Anyway, I wanted to see if I
could capture it more clearly. And there are different ways
besides this little smoke cell. Another option is particles
suspended in a liquid. That reminded me of a video I made about why white things are white. In it I showed the Uzo effect. One clear liquid poured
into another turns cloudy. It's cloudy because the
liquid is now scattering light and it's scattering light because it is full of
tiny suspended particles. The oils in the Uzo form
an emulsion with the water. So maybe I could see those tiny Uzo balls under the microscope
and watch them jiggle. In the end they were just too small for me to be able to see
even with a microscope. But it's okay because I
noticed something similar with a different liquid, this dry skin treatment called hydromol. It also turns cloudy
when you add it to water. And to me that's a much clearer effect than what you get from the smoke cell, perhaps because the particles don't keep coming in and
out of the focal plane. But in any case, it's good to confirm that Brownian motion happens
in gases and in liquids. Another option is plain old milk. Milk is in emulsion to, actually,
it contains fat globules. They're about one or two microns,
but also casein micelles, and they're quite a bit
smaller under a micron. So we should potentially be able to see two different levels of Brownian motion. And actually it does seem that way. The bigger particles seem to jiggle less than the smaller particles. Interestingly, when Dot Brown
first observed this in 1827, he wanted to eliminate the possibility that what he was seeing
was biological in nature. I mean, it's not an
unreasonable possibility. Like look at these Daphnia
under a microscope. The movement isn't that different. And he was viewing the jiggles of pollen particles after all. So perhaps they were moving
because they were alive. Actually, pollen is typically too big to have a visible brownian jiggle. But Brown saw the pollen particles eject even smaller particles outta themselves, and he saw a jiggle in those. But just to be sure he wasn't looking at
motile little critters. He picked up a quartz crystal. Quartz very occasionally has water and air trapped inside it. That's called anhydroquartz. And typically that water will
have been trapped in there for thousands of years. So if there ever was
anything alive in there, it was certainly dead by now. That sounded like a really cool idea. So I picked up my own
bit of anhydroquartz. That curved edge you can see in there is a boundary between water
and air inside the crystal. Unfortunately, I just couldn't get focused that deep inside the crystal, so this is a complete fail. We'll take Brown's word
for it on that one. Back then, people didn't know about atoms. But now we know that these
tiny jiggling particles are surrounded by loads
of atoms zooming around, and as they zoom around, they
smack into the particles. We typically don't notice the effect of these individual collisions
in our everyday life. That's because there are
just so many of them. Like there are just as many collisions of air molecules happening on the left side of this rubber ball as there are happening on the right side of this rubber ball. So the rubber ball goes nowhere, but on a much smaller scale, because these collisions are random, you will occasionally have more and stronger collisions on
one side than the other. And so the particle gets
knocked about in a visible way. By the way, it's still an
insane number of collisions, like a single molecule of water collides with other water molecules, 10 to the 14 times per second. You might be thinking
with that many collisions, surely it would average out to zero net visible effect on something the size of a micron. The reason it doesn't is because of the insane
speeds of water molecules. At room temperature, the
speed of a water molecule smacking into one of these particles could be anywhere between
zero meters per second and several hundred meters per second. With that much variation, it's no surprise that you'll occasionally
get a decent imbalance from one side to the other
of one of those particles. What you're seeing here is a
small model of that process. I have a dish full of tiny ball bearings that I'm jiggling to
simulate the motion of, for example, water molecules. And this plastic bead is like a particle suspended in that liquid. And you can see how the
individual collisions with the ball bearings
cause the plastic particle to move around. But because the motion
of the plastic beads is averaged over lots
of little collisions, the motion of the bead
is a lot less dramatic than the individual motions
of the ball bearings, just like with real Brownian motion. It's also helpful to see
an animation of that. See how individual collisions
from smaller molecules cause the larger particle
to jiggle around? If you couldn't see the smaller molecules, that larger particle would
seem to have a life of its own. And you can see that as
the particle gets larger, the effect is reduced, and in the opposite direction, if the particle gets smaller,
the effect is increased. So what was the genius
thing that Einstein did with Brownian motion? Well, in 1905, the idea that
matter was made of atoms was starting to gain traction. But still, there were a
lot of respected scientists that didn't believe in atoms
and molecules, Einstein did. And when he was thinking
about Brownian motion, he made a brilliant assumption about the way atoms and molecules move. He said, let's assume that
molecules that you can't see and particles that you can
see under a microscope, they move according to the
same principles and rules. It's just that they differ in size. That means that Einstein was able to take equations
from the physics of fluids and apply them to this
thing that we can see. You combine those equations
into an expression for something called the
diffusion coefficient, which is like a measure of how fast does something diffuse through a fluid. The great thing about this equation is a lot of these terms are
things we can measure. You've got things like
viscosity of the liquid, something you can measure. You've got the radius of
the suspended particles, again, something you can measure. The only things you can't measure are the diffusion coefficient
and Avogadro's number. That means if we can
measure either one of those, we can calculate the other. In other words, if we can measure
the diffusion coefficient, we can calculate Avogadro's number, and Avogadro's number would
be an amazing thing to know. Avagadro's number tells us, for example, exactly how many atoms
of hydrogen there are in one gram of hydrogen. And if you divide one gram by that number, you then know the exact massive hydrogen. How cool is that? So if we want Avogadro's number, we need the diffusion coefficient. So how are we gonna get that? Well, here's the genius part. Einstein realized that we can calculate the diffusion coefficient
of these tiny particles by observing them move. Brownian particles move in the same way as what mathematicians call a random walk. In other words, the particles
move a random distance in a random direction after
every fixed time period. And then Einstein said, look, well, if we can record the
motion of these particles, measure how far they travel on average over a set time period, we can then get a value for
this diffusion coefficient. So Einstein was able to take equations from the world of things that we can't see and apply them to things that we can see. And then he was able to figure out a way to measure one of the unknown
terms in that equation by observing those things that we can see. And that is the bridge between two worlds that Brownian motion creates. Three years later, Jean
Perrin actually conducted that experiment and
calculated Avogadro's number to be 7.15 times 10 to the 23. We now know it to be
6.02 times 10 to the 23. Hey, I mean, that's not bad, is it? There's one really interesting thing I want to say about Avogadro, but first, can we just take a minute to recognize how
unbelievable Einstein was? I mean, it's obvious, I suppose. But to hammer the point home, he published three
papers in one year, 1905. One on relativity, one on
the photoelectric effect, he won the Nobel Prize for that one. And of course, his theory of
relativity changed everything. But that third paper that he
published in the same year, the one about Brownian motion helped to convince the world
about atoms and molecules. And at the same time, he gave us a way to actually calculate the mass of atoms. It's unbelievable. That's why they call 1905
Einstein's annus mirabilis, which is Latin for anus mirror balls. I think it's like an exclamation. Like if you see something amazing, you go, oh wow, three papers
in one year, anus mirror balls! Back to Avogadro though. Something surprising about gases is it doesn't matter how heavy the individual atoms or
molecules of a gas are. If you have a certain volume of a gas at a specific temperature and pressure, then you will have the same number of atoms or molecules of that gas regardless of what the gas is. So at room temperature and pressure, 22.4 liters of a gas will contain an Avogadro's
number of molecules. Just playing with the numbers a bit, that means that this
syringe that I've drawn 3.6 milliliters of air into, and this one that has 3.6
milliliters of carbon dioxide, and this one that has
3.6 milliliters of helium all have 100 million
trillion atoms in them, regardless of the fact that they all weigh different amounts. That's weird, isn't it? Brown, Einstein, and Perrin looked at a complex and seemingly random process and were able to discern
the profound truth that lay beneath. Which reminds me, I really
wanna tell you about Jane Street's Academy
of Math and Programming that is now accepting applications for the summer 2024 program. It's a no-cost educational program for recent high school graduates interested in maths and computer science, who have also experienced barriers to accessing advanced STEM
educational opportunities. It's a program run by Jane Street, a company that looks at the complex and seemingly random world of finance and finds the profound
truths that lie beneath. They're like Brown, Einstein
and Perrin, but for money. The curriculum focuses on mathematics, computer programming, data
analysis, game theory, and more. It's a five week in-person
program in New York, but they're accepting applications
from all over the world. Not only is travel paid for, but food and accommodation is as well. And successful applicants will receive $5,000 scholarship towards
their further education. To celebrate the opening
of this year's application, Jane Street have put together
a New York City themed logic puzzle to wet your appetite. If you do solve it, feel free to include the
solution in your application. You don't need to solve
the puzzle to apply, it's just a bit of fun. The puzzle is at the
link in the description along with everything
else you need to apply. Applications close on the 13th of March so check out the AMP program today. I hope you enjoyed this video. If you did, don't forget to hit subscribe and the algorithm thinks
you'll enjoy this video next. (upbeat music)
