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And these quantized electron energy level such as observed in the Franck-Hertz experiment
and proposed and used in an ad hoc fashion by Bohr in his atomic model
kind of suggests that electrons are a wave
forming standing waves inside the atom, thus giving you the specific spacing and the harmonics
so why not?
De Broglie said exactly that
by the way, his name is, according to a French person, pronounced ...
he was thinking since light have
wave properties and particle properties as we have discussed earlier, this wave-particle duality
why can't this also work for all kinds of matter, including electrons
so to apply the wave-particle duality for matter, what he needed was
a wavelength because we already have this expression: we have E = hv
so we know what frequency we can talk about, but what's the wavelength?
because we don't know anything about these waves, we don't know about
their phase velocity, we may know as a group how fast it is moving, that's the group velocity
but we have to use the phase velocity to use v=f*lambda
so we need some other way to find lambda
For a photon, what else do we know about the photon
well we know that its energy is also, through special relativity,
E = mc^2
once you take out the rest mass m_0
it becames this and this applies of course for the photon, because a photon travels
at the speed of light which is by definition relativistic
and the rest mass it has is 0
so, you can relate its energy to momentum
so as a particle, photon has momentum, you can actually observe this by shining a very intensed focused laser beam
at a small mass, like a reflective sphere that is very small and light
so from this, we can actually
for the photon, we know the photon's [phase] speed, which is c
and so combining these things
we know that
...
so lambda is related to the momentum of the photon,
whereas the frequency, as I've said before, is related to the energy of the photon both by Planck's constant
what if we apply this to matter as well; matter has energy; matter has momentum
we can equally work out the frequency and the wavelength for matter and then talk about them in terms of waves
just to get a sense of these numbers
for an electron at different energies
so of course knowing energy and mass, we can work out the speed and momentum as well, thus getting the wavelength
so if we have energy
of 1 eV [electronvolt] meaning we take an electron and accelerate it through 1 V
we get 12.3 Angstrom, and an Angstrom is equal to
10^-10 m, useful unit for talking about atomic spaces
you get to 10 eV
wavelength continues to get shorter and shorter
and even at 1 eV
12.3 Angstrom, that's like the size of 12
roughly 12 hydrogen atoms, it's not very big
so that's why most cases we have tried and observed an electron
the wavelength is so small we don't see it acting as a wave
because the wavelength is small
what we will need then in order to see
these kind of wavelengths, by the way, is similar to x-ray wavelength, so it passes through a lot of matter
where it comes into the play as a wave and you see interference is that you have crystal spacing
and it is precisely in these types of experiments
where we can see
wave properties of electron
and finally
it was done in 1927 by Davisson and Germer, again two different experimentalists, two different people
also, around the same time
by Mr. Thompson as well
so Thompson did a transmission diffraction through a thin foil and saw diffraction rings
and Davisson and Germer had crystaline planes forming more or less like a thin film interferences
but more precisely, it's a diffraction grating as well
and we will look at the Davisson-Germer experiment in more detail in our demo
and much much later, in the 1960s finally were able to also build
double slits that are small enough for the electrons and observing the interference from it
with all these observations, it was pretty much undisputable that electrons also have wave behavior
and so proving the existence of matter waves
now what exactly are these waves of?
In the sense that when we have sound waves, they were waves of pressure or longitudinal displacement
when you have EM waves, they are oscillation in electric fields and magnetic fields
what are these matter waves of?
before that, I'd like to refer you to this next video which shows you what happens in a
electron [interference] experiment