Hi. It’s Mr. Andersen and this is AP Physics essentials video 128. It is matter as a wave.
In the last video I showed how the work of Louis de Broglie suggested that matter might
be made of waves. Just like light is made of particles. And he even came up with de
Broglie’s wavelength which is equal to Planck’s Constant divided by momentum, which is mass
times velocity. The reason we do not see matter as a wave is that it has such a large mass
compared to Planck’s constant that the wavelength is so small that we do not really see it.
But to show that it was a wave, a couple of scientists, Davvison and Germer devised a
neat experiment where they showed interference as electrons were interfering with one another.
Electrons are matter and they were behaving like waves. What are some implications of
that? Well an electron microscope uses that really small wavelength of electrons to see
things that we could not see with visible light. And so matter is both a wave and a
particle. It has wave-particle duality just like light. And so if we treat matter as a
particle that is classical mechanics. And if we treat it like a wave that is quantum
mechanics. But which world should we live in all depends on scale. If it is large we
call that classical mechanics. And if it is very very small, nanoscopic, that is the world
of quantum mechanics. And de Broglie’s wavelength is kind of a determiner of which area we should
be along this continuum. And then the Davvison Germer showed that he have actually right.
And so let’s apply the de Broglie wavelength to a large object, like a baseball. And so
it is equal to Planck’s constant divided by momentum. Remember momentum is simply mass
times velocity. If I know the mass of the object, the velocity of the object, I simply
plug those in and I get a de Borglie wavelength that is incredibly small, 10 to the negative
34. To give you some sense of scale the diameter of a hydrogen atom is only 10 to the negative
11 and now we are dealing with 10 the negative 34. And so this implies that the wavelength
is so small that we essentially could not even measure it, could not even see it. But
now instead of a baseball let’s look at an electron that is just moving through a
simply circuit. It has an incredibly small mass, a larger velocity, but let’s plug
that into our equation. And now we get a de Broglie wavelength that is going to be not
as small. You know since we have momentum on the bottom, as we decrease the mass relative
to Planck’s constant we get a wavelength that is going to be larger, on the order of
1.2 nanometers. And as we move into the nanoscopic world, those nanometers, we are moving into
wavelengths that are close to the wavelengths of visible light. Remember visible light would
be, green light is going to be somewhere around 500 nanometers. And so that is why we have
better resolution with an electron microscope. But it also means that we have to start treating
small particles like electrons as a wave, not as a particle. So one thing that waves
can do that particles can not is they can interfere. And so if I have two waves next
to each other, as they oscillate there are going to be certain areas where the waves
will destructively interfere with each other. In other words they are going to break each
other down. And areas where they are going to build each other up. And particles do not
do that. They can not interfere. So Davvison and Germer, in their experiment, were looking
for interference in electrons. And so inside a vacuum chamber they had an electron gun
that would produce an electron beam that would strike a nickel target. Now what was interesting
is that nickel target built up some oxidation on it so they put it in an oven and inadvertently
what they did is created one large crystal which actually helped them get good results.
As the electron hit the nickel it would then scatter the electrons and the electrons, they
hoped, would interfere with one another. They had a movable detector that as it moved back
and forth at different angles, they hoped, it would receive different amounts of electrons,
so there would be interference of those electron matter waves. And so if you visualize it like
this, there are going to be along the pathway of that detector areas where we are going
to have more electrons, areas where we are going to have less electrons. So they are
looking for direct evidence that matter acts as a wave. And this is their data. They found
at different angles they would have more or less amounts of this electric charge and therefore
the electrons were interfering with one another. And so did you learn to predict the dependence
of the de Broglie wavelength on both the mass and the velocity? And then can you see that
the Davvison-Germer experiment showed interference in electrons and therefore showed that those
electron’s matter were acting as waves? I hope so and I hope that was helpful.