De-Broglie’s Hypothesis Video Lecture - Civil Engineering (CE)

so in the early 20th century physicists
were bamboozled because light which we
thought was a wave started to behave in
certain experiments as if it were a
particle so for instance there was an
experiment done called the photoelectric
effect where if you shine light at a
metal it'll knock electrons out of the
metal if that light has sufficient
energy but if you tried to explain this
using wave mechanics you get the wrong
result and it was only by resorting to a
description of light as if it could only
deliver energy in discrete packets that
Einstein was able to describe how this
photoelectric effect worked and predict
the results that they actually measure
in the lab in other words light was only
giving energy in certain bunches equal
to something called Planck's constant
multiplied by the frequency of the light
it either gave all of this energy to the
electron or it gave none of the energy
of the electron it was never
half-and-half it never gave half of this
energy it was sort of all or nothing but
this was confusing to people because we
thought we had established that light
was a wave and we thought that because
if you shine light through a double slit
if it were a particle if light were just
a bunch of particles you would expect
particles to just either go through the
top hole and give you a bright spot
right here or go through the bottom hole
give you a bright spot right here but
what we actually measure when you do
this experiment with light is that the
light seemingly diffracts from both
holes overlaps and it gives you a
diffraction pattern on the screen so
instead of just two bright spots it
gives you this constructive and
destructive pattern that would only
emerge if the light beam were passing
through both slits and then overlapping
the way waves would out of two holes on
this other side of the double flip so
this experiment showed that light
behaved like a wave but the
photoelectric effect showed that light
behaved more like a particle and this
kept happening you kept discovering
different experiments that showed
particle-like behavior or different
experiments that showed wave-like
behavior for light finally physicists
resigned to the fact that light can
seemingly have particle-like properties
and wave-like properties depending on
the experiment being conducted
so that's where things sat when in 1924
a young French physicist a brilliant
young physicist named Louise de bruit
now it looks like you pronounce this
louise de Broglie that's what he said I
always read this and I said de Broglie
in my mind and I knew that wasn't right
if you look it up it's more like Louie
de bruit so get rid of all that replace
it with a Y in your mind Louie de broy
in 1924 wrote a paper and he did
something no one else was doing everyone
else was worried about light and light
behaving like a particle or a wave
depending on the experiment what we do
bro I said this what about the electron
you got this electron flying off here he
said if light which we thought was a
wave connect like a particle
maybe electrons which we thought were
particles can act like a wave in other
words maybe they have a wavelength
associated with them he was trying to
synthesize these ideas into one
overarching framework in which you could
describe both quanta of light ie
particles of light and particles which
we thought were just particles but maybe
they can behave like waves as well so
maybe he was saying everything in the
universe can behave like a particle or a
wave depending on the experiment that's
being conducted and he set out to figure
out what would this wavelength be he
figured it out it's called the debroglie
wavelength oh I reverted sorry dubrow
wavelength not the de Broglie wavelength
the debroglie wavelength he figured it
out and he realized it was this so he
actually postulated it he didn't really
prove this he motivated the idea and
then it was up to experimentalist to try
this out so he said that the wavelength
associated with things that we thought
were matter so sometimes these were
called matter waves but the wavelength
of say an electron is going to be equal
to Planck's constant divided by the
momentum of that electron and so why did
he say this why did he pick Planck's
constant which by the way if you're not
familiar with Planck's constant it is
like the name suggests just a constant
and it's always the same value it's six
point six to six times 10 to the
negative 34
it's really small this was a constant
discovered in other experiments like
this photoelectric effect and the
original blackbody experiments that
Planck was dealing with called Planck's
constant it shows up all around modern
physics and quantum mechanics so how did
Louise Dubrow even come up with this why
why Planck's constant over the momentum
well people already knew for light that
the wavelength of a light ray is going
to also equal Planck's constant divided
by the momentum of the photons in that
light ray so the name for these
particles of light called photons I'm
drawing them localized in space here but
don't necessarily think about it that
way think about it just in terms of they
only deposit their energy in bunches
they don't necessarily have to be at a
particular point at a particular time
this is a little misleading this picture
here I'm just not sure how else to
represent this idea in a picture that
they only deposit their energies in
bunches so this is a very loose drawing
don't take this too seriously here so
people had already discovered this
relationship for photons and that might
bother you you might be like wait a
minute how in the world can photons have
momentum they don't have any math I know
momentum is just M times V if the mass
of light is 0 doesn't I mean the
momentum always has to be 0 wouldn't
that make this wavelength infinite and
if we were dealing with classical
mechanics that would be right but this
is turns out this is not true when you
travel near the speed of light because
parallel to all these discoveries in
quantum physics Einstein realized that
this was actually not true when things
traveled near the speed of light the
actual relationship I'll just show you
it looks like this the actual
relationship is that the energy squared
is going to equal the rest mass squared
times the speed of light to the fourth
plus the momentum of the particle
squared times the speed of light squared
this is the better relationship that
shows you how to relate momentum and
energy this is true in special
relativity and using this you can get
this formula for the wavelength of light
in terms of its momentum it's not even
that hard
in fact I'll show you here it only takes
a sec
light has no rest mass we know that
light has no rest mass so this term is
zero we've got a formula for the energy
of light which is H times F so e squared
is just going to be H squared times F
squared the frequency of the light
squared so that equals the momentum of
the light squared times the speed of
light squared I can take a square root
of both sides now get rid of all these
squares and I get HF equals momentum
times C if I rearrange this and get H
over P on the left hand side if I divide
both sides by momentum and then divide
both sides by frequency I get h over the
momentum is equal to the speed of light
over the frequency but the speed of
light over the frequency is just the
wavelength and we know that because the
speed of a wave is wavelength times
frequency so if you solve for the
wavelength you get the speed of the wave
over the frequency and for light the
speed of the wave is the speed of light
so C over frequency is just wavelength
that is just this relationship right
here so people knew about this and de
Broglie suggested hypothesize that maybe
the same relationship works for these
matter particles like electrons or
protons or neutrons or things that we
thought were particles maybe they also
can have a wavelength and you still
might not be satisfied you might be like
what what does that even mean that a
particle can have a wavelength as hard
to even comprehend how would you even
test that well you test it the same way
you test whether photons and light can
have a wavelength you subject them to an
experiment that would expose the
wave-like properties ie just take these
electrons shoot them through the double
slit so if light can exhibit wave-like
behavior when we shoot it through a
double slit then the electrons if they
also have a wavelength and wave-like
behavior they should also demonstrate
wave-like behavior when we shoot them
through the double slit and that's what
people did there was an experiment by
Davidson and Germer they took electrons
they shot them through a double slit if
the electrons just created two bright
electrons splotches right behind the
holes you would have known that okay
that that's not wave-like these are just
flat-out particles debris was wrong
but that's not what they discovered
Davidson and Germer did
this experiment and it's a little harder
you can't I mean the wavelength of these
electrons are really small so you've got
to use atomic structure to create this
double slit it's difficult you should
look it up interesting people still use
this called electron diffraction but
long story short they did the experiment
they shot electrons through here guess
what they got they got wave-like
behavior they got this diffraction
pattern on the other side and when they
discover that the boy won his Nobel
Prize because it showed that he was
right
matter particles can have wavelength and
they can exhibit wave-like behavior just
like light can which was a beautiful
synthesis between two separate realms of
physics matter and light turns out they
weren't so different after all now
sometimes the boy is given sort of a bum
rap people say wait a minute all he did
was take this equation that people
already knew about and just restate it
for matter particles and no that's not
all he did if you go back and look at
his paper I suggest you do he did a lot
more than that the paper is impressive
it's an impressive paper and it's
written beautifully he did much more
than this but this is sort of the thing
people most readily recognize him for
and to emphasize the importance of this
before this point people had lots of
ideas and formulas in quantum mechanics
they didn't completely understand after
this point after this pivot where we
started to view matter particles as
being waves previous formulas that
worked for reasons we didn't understand
could now be proven in other words you
could take this formula an idea from
debris and show why Bohr's atomic model
actually works and shortly after
dubrow's paper Schrodinger came around
and basically set the stage for the
entire rest of quantum physics and his
work was heavily influenced by the ideas
of Louis de bruit so recapping light can
have particle like or wave-like
properties depending on the experiment
and so can electron the wavelength
associated with these electrons or any
matter particle can be found by taking
Planck's constant divided by the
momentum of that matter particle and
this wavelength can be tested in
experiments
electrons exhibit wave-like behavior and
this formula accurately represents the
wavelength that would be associated with
the diffraction pattern that emerges
from that wave-like behavior