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- [Narrator] So in the early 20th century,

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physicists were bamboozled because light,

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which we thought was a wave,

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started to behave in certain experiments

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as if it were a particle.

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So, for instance, there
was an experiment done

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called the photoelectric effect,

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where, if you shine light at a metal,

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it'll knock electrons out of the metal

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if that light has sufficient energy,

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but if you tried to explain
this using wave mechanics,

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you get the wrong result.

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And it was only by resorting
to a description of light

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as if it could only deliver
energy in discrete packets

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that Einstein was able to describe

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how this photoelectric effect worked,

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and predict the results

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that they actually measure in the lab.

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In other words, light
was only giving energy

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in certain bunches,

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equal to something called planks constant,

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multiplied by the frequency of the light.

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It either gave all of this
energy to the electron,

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or it gave none of the
energy to the electron.

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It was never half and half.

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It never gave half of this energy,

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it was sort of all or nothing.

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But this was confusing to people.

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'Cause we thought we had established

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that light was a wave,

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and we thought that
because if you shine light

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through a double slit,

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if it were a particle,

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if light were just a bunch of particles,

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you would expect particles

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to just either go through the top hole

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and give you a bright spot right here,

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or go through the bottom hole,

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give you a bright spot right here,

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but what we actually measure

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when you do this experiment with light,

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is that the light seemingly
diffracts from both holes,

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overlaps, and it gives you

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a diffraction pattern on the screen.

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So instead of just two bright spots,

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it gives you this constructive
and destructive pattern

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that would only emerge if the light beam

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were passing through both slits,

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and then overlapping, the way waves would,

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out of two holes on this
other side of the double slit.

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So this experiment showed that
light behaved like a wave,

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but the photoelectric effect showed

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that light behaved more like a particle,

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and this kept happening.

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You kept discovering different experiments

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that showed particle-like behavior,

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or different experiments

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that showed wave-like behavior for light.

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Finally, physicists resigned to the fact

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that light can seemingly have
particle-like properties,

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and wave-length properties,

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depending on the
experiment being conducted.

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So that's where things sat when in 1924,

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a young French physicist, a
brilliant young physicist,

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named Louis de Broglie,

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now, it looks like you pronounce
this "Louis de Broe-glee",

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and that's what I always said.

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I always read this and I said
"de Broe-glee" in my mind,

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and I knew that wasn't right.

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If you look it up, it's
more like "Louis de Broy",

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so get rid of all that, replace
it with a "y" in your mind,

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Louis de Broglie, in 1924, wrote a paper,

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and he did something
no one else was doing.

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Everyone else was worried about light,

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and light behaving like
a particle or a wave,

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depending on the experiment;

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Louis de Broglie said this,
"What about the electron?

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"You got this electron flying off here,"

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he said, "if light, which
we thought was a wave,

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"can act like a particle,

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"maybe electrons, which
we thought were particles,

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"can act like a wave."

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In other words, maybe
they have a wavelength

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associated with them.

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He was trying to synthesize these ideas

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into one over arching framework

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in which you could describe
both quanta of light,

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i.e. particles of light, and particles,

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which we thought were just particles,

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but maybe they can behave
like waves as well.

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So maybe, he was saying,
everything in the universe

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can behave like a particle or a wave,

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depending on the experiment
that's being conducted.

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And he set out to figure out
what would this wavelength be,

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he figured it out, it's called
the "de Broe-lee" wavelength,

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oh, I reverted, sorry,

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"de Broy" wavelength, not the
"de Broe-glee" wavelength.

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The de Broglie wavelength,
he figured it out,

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and he realized it was this.

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So, he actually postulated it.

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He didn't really prove this.

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He motivated the idea,

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and then it was up to
experimentalists to try this out.

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So he said that the wavelength associated

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with things that we thought were matter,

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so sometimes these were
called matter waves,

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but the wavelength of, say, an electron,

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is gonna be equal to Planck's constant,

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divided by the momentum of that electron.

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And so, why did he say this?

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Why did he pick Planck's constant,

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which, by the way,

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if you're not familiar
with Planck's constant,

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it is like the name
suggests, just a constant,

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and it's always the same value,

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it's 6.626 times 10,

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to the negative 34th joule seconds.

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It's really small.

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This was a constant discovered
in other experiments,

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like this photoelectric effect,

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and the original blackbody experiments

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that Planck was dealing with.

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It's called Planck's constant,

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it shows up all around modern
physics and quantum mechanics.

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So how did Louis de Broglie
even come up with this?

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Why Planck's constant over the momentum?

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Well, people already knew for light,

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that the wavelength of a light ray

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is gonna also equal Planck's constant,

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divided by the momentum of
the photons in that light ray.

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So the name for these particles
of light are called photons.

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I'm drawing them localized in space here,

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but don't necessarily
think about it that way.

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Think about it just in terms of,

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they only deposit their energy in bunches.

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They don't necessarily have to be

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at a particular point
at a particular time.

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This is a little misleading,
this picture here,

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I'm just not sure how else
to represent this idea

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in a picture that they only deposit

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their energies in bunches.

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So this is a very loose drawing,

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don't take this too seriously here.

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But people had already discovered

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this relationship for photons.

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And that might bother
you, you might be like,

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"Wait a minute, how in the
world can photons have momentum?

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"They don't have any mass.

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"I know momentum is just m times v,

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"if the mass of light is zero,

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"doesn't that mean the
momentum always has to be zero?

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"Wouldn't that make this
wavelength infinite?"

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And if we were dealing
with classical mechanics,

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that would be right,

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but it turns out, this is not true

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when you travel near the speed of light.

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Because parallel to all these

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discoveries in quantum physics,

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Einstein realized that
this was actually not true

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when things traveled
near the speed of light.

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The actual relationship,
I'll just show you,

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it looks like this.

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The actual relationship is
that the energy squared,

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is gonna equal the rest mass squared,

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times the speed of light to the fourth,

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plus the momentum of
the particles squared,

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times the speed of light squared.

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This is the better
relationship that shows you

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how to relate momentum and energy.

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This is true in special relativity,

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and using this, you can get this formula

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for the wavelength of light
in terms of its momentum.

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It's not even that hard.

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In fact, I'll show you here,
it only takes a second.

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Light has no rest mass, we know that,

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light has no rest mass,
so this term is zero.

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We've got a formula for
the energy of light,

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it's just h times f.

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So e squared is just gonna
be h squared times f squared,

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the frequency of the light squared,

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so that equals the momentum
of the light squared,

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times the speed of light squared,

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I could take the square
root of both sides now

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and get rid of all these squares,

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and I get hf equals momentum times c,

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if I rearrange this, and get h
over p on the left hand side,

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if I divide both sides by momentum,

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and then divide both sides by frequency,

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I get h over the momentum

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is equal to the speed of
light over the frequency,

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but the speed of light over the frequency

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is just the wavelength.

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And we know that, because
the speed of a wave

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is wavelength times frequency,

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so if you solve for the wavelength,

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you get the speed of the
wave over the frequency,

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and for light, the speed of
the wave is the speed of light.

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So c over frequency is just wavelength.

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That is just this relationship right here.

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So people knew about this.

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And de Broglie suggested, hypothesized,

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that maybe the same relationship works

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for these matter particles
like electrons, or protons,

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or neutrons, or things that
we thought were particles,

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maybe they also can have a wavelength.

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And you still might not be satisfied,

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you might be like, "What,
what does that even mean,

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"that a particle can have a wavelength?"

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That's hard to even comprehend.

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How would you even test that?

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Well, you'd test it the same way you test

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whether photons and light
can have a wavelength.

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You subject them to an experiment

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that would expose the
wave-like properties,

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i.e., just take these electrons,

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shoot them through the double slit.

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So, if light can exhibit
wave-like behavior

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when we shoot it through a double slit,

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then the electrons, if
they also have a wavelength

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and wave-like behavior,

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they should also demonstrate
wave-like behavior

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when we shoot them
through the double slit.

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And that's what people did.

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There was an experiment
by Davisson and Germer,

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they took electrons, they shot
them through a double slit.

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If the electrons just created
two bright electron splotches

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right behind the holes,
you would've known that,

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"Okay, that's not wave-like.

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"These are just flat out
particles, de Broglie was wrong."

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But that's not what they discovered.

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Davisson and Germer did this experiment,

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and it's a little harder,

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the wavelength of these
electrons are really small.

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So you've gotta use atomic structure

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to create this double slit.

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It's difficult, you should
look it up, it's interesting.

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People still use this, it's
called electron diffraction.

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But long story short,
they did the experiment.

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They shot electrons through here,

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guess what they got?

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They got wave-like behavior.

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They got this diffraction
pattern on the other side.

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And when they discovered that,

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de Broglie won his Nobel Prize,

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'cause it showed that he was right.

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Matter particles can have wavelength,

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and they can exhibit wave-like behavior,

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just like light can,

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which was a beautiful synthesis between

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two separate realms of
physics, matter and light.

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Turns out they weren't
so different after all.

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Now, sometimes, de Broglie
is given sort of a bum rap.

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People say, "Wait a minute, all he did

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"was take this equation that
people already knew about,

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"and just restate it
for matter particles?"

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And no, that's not all he did.

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If you go back and look at
his paper, I suggest you do,

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he did a lot more than that.

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The paper's impressive,
it's an impressive paper,

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and it's written beautifully.

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He did much more than this,

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but this is sort of the thing

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people most readily recognize him for.

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And to emphasize the importance of this,

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before this point,
people had lots of ideas

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and formulas in quantum mechanics

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that they didn't completely understand.

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After this point, after this pivot,

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where we started to view matter
particles as being waves,

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previous formulas that worked,

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for reasons we didn't
understand, could now be proven.

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In other words, you
could take this formula

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and idea from de Broglie,

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and show why Bohr's atomic
model actually works.

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And shortly after de Broglie's paper,

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Schrodinger came around and basically

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set the stage for the entire
rest of quantum physics.

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And his work was heavily influenced

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by the ideas of Louis de Broglie.

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So recapping, light can have

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particle-like or wave-like properties,

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depending on the experiment,

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and so can electrons.

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The wavelength associated
with these electrons,

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or any matter particle,

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can be found by taking Planck's constant,

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divided by the momentum
of that matter particle.

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And this wavelength can
be tested in experiments,

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where electrons exhibit
wave-like behavior,

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and this formula accurately
represents the wavelength

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that would be associated
with the diffraction pattern

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that emerges from that wave-like behavior.