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Current time:0:00Total duration:11:20

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

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