Blackbody Radiation, Modern Physics, Quantum Mechanics, and the Oxford Comma | Doc Physics

in the year 1900 respected physicist Lord Kelvin said there is nothing new to be discovered in physics now all that remains is more and more precise measurement now with that kind of stuff would you want to become a physicist this sounds pretty boring let's measure more and more precisely okay now let's do it again with a new tool great so here's the thing this was about as wrong as he could possibly be because in the next 25 years all of physics would be turned on its head by two amazing new theories that really caused people to investigate what life was what the universe was what perception means and how consciousness plays into physics these are very big questions and Lord Kelvin sure called it wrong in fact he had a big part in actually flipping physics over on his head so let's go to those two things that he had he had a couple hesitations he referred to them as dark clouds and one of them was the michelson-morley experiment Mickelson and Morley were trying to measure the ether they were trying to see how light traveled through space because waves require a medium through which to travel and they wanted to know if they could see the fact that earth was sometimes see earth is right and well that's the Sun and Earth is going like this so sometimes what's going that way and sometimes Earth's going that way they were hoping and they really ought to have been able to measure our velocity through the ether this way at one time of the year and the other way at the other time the year or in fact just a velocity at all through the ether what are the odds that were perfectly at rest to the ether pretty much zero even if we are at rest relative to ether that's the ether is this thing that light has to travel through even if we are at rest relative the ether then if you send light this way and some light that way then what are the odds that those lights are going to experience exactly the same pattern through the ether I don't know ether is an interesting idea but Wow was that wrong so they couldn't explain the mickelson Morley experiment with the fact that waves go through the vacuum of space there seem to be some strange implications there and blackbody radiation and our subject today is black bodies so consider consider for me if you will a black body I can safely say that all of modern physics comes from sitting around and considering black bodies here is a picture of a black body the idea is that it is a cavity and there's a very very small opening so if we send a ray of light into this cavity then let's say it's going this direction it will go into the cavity and bounce around and every time there's a bounce you would certainly agree that each bounce carries a finite probability of being absorbed so let's say it's bounced around 70 times or something it has probably been absorbed as long as this opening here is very small the idea of a black body is such that light that comes in cannot get out as reflected light so you know when you're looking at stuff like your computer screen well not your computer screen dang it if you look at a flower pot sitting over there you know the reason that you see the flower pot is because that flower pot is reflecting light towards your eyes don't talk about your computer screen right now my point is the black body will never reflect light towards your eyes so in fact if you look at a black body you actually see it's true light that is coming from within it and maybe you didn't know that when things are hot they glow but this is true when things are hot they do in fact glow so black bodies let out light in fact since no reflected light gets out of a black body the black bodies light is its own true light and it's a characteristic thing but the cool thing about black bodies is they don't have to be this hollow box with a tiny hole poked in it that's smeared with charcoal on the inside so it's not very reflective at all and we try to absorb even with 70 hits of even if it were a mirror and this hole is really tiny you could still get it to be a black body but we want to coat it with black to make it as a deal as possible the thing is in the infrared wavelengths my skin is black look at it my skin is absorbing all the infrared that's hitting it to a large degree so let's consider let's consider the problem this is the problem that Lord Kelvin was aware he said intensity this is what was known intensity as derived by oh who were these guys we're talking about oh shoot rally and jeans the rally jeans law says that if if you're looking for the intensity of a black box that's radiating power out of it wait can we talk a little bit more about the fact that things have certain colors you ever heard of something that's red hot yeah if you've got a red hot piece of metal then it will be glowing red and that's because some of its energy that it's emitting all the time is coming out as light energy that you can see a lot of it is coming out as infrared which is why you can feel things are hot if you get close to them even if they're not glowing hot that makes stove's a little bit dangerous and soup to soups a little bit dangerous but if you've got something that's even hotter maybe you've heard of the phrase white hot something that's white hot is even hotter because it's not just spitting out red it's also spitting out higher frequencies and therefore higher energies of light are present so that's the idea behind this sensor right here it's an infrared thermometer if I turn it on and measure the temperature of the table right here I find the temperature of the table to be twenty four point six Celsius and I put it in my armpit watch that oh yeah my armpit is 30.6 Celsius okay so that means that by looking at the color of light coming into this lens right here it's able to calculate the temperature where it's pointing Wow that's pretty fancy it's using some of the physics that we're studying today so we've got two times the frequency score times this constant right here was Boltzmann's constant we've seen it already a little bit with the kinetic theory of gases and here's temperature and we have to divide it by the speed of light score so this is a classically derived intensity that we would expect to be happening if we look into this black box and let me graph what this looks like this says that the intensity gets higher as the frequency gets higher and in fact it says that the intensity doesn't ever get low as the frequency gets higher so I mean that may be a little bit redundant but I want to point out what this is looking like here I'm going to put this I put it intensity in quotes because it's actually radians which is a straight e and you divide by the cosh it's complicated I don't want to talk about it I'm just going to call this intensity right here it's kind of a scaling factor probably a 4 PI squared or something so here's frequency frequency F and intensity is supposed to get bigger by the square of the frequency so let's give ourselves a little purple things show what this is doing this is a quadratic relationship the only I mean I don't have any real problem of quadratic relationships except that white costs energy and this is in units of kind of because of the straight ian's thing it's kind of units watts per square meter so I'm saying if you look in this whole this prediction of the rally jeans equation says that if you look in the whole your eye will be melted by the enormous amount of high frequency radiation that's coming out in fact you guys go to integrals can you integrate this sucker for me give me some both some Riemann sums here Eman the sum out that way that is infinite it looks even bigger than infinity because it's getting bigger this way too that is an infinite amount of energy and this is gently called the ultraviolet catastrophe it's very high frequencies so those imply sort of ultraviolet and this is a disaster or as it was called at the time and still called now a catastrophe problem is it's not real this law so miserably fails at describing what's actually happening because what's actually happening looks like seafoam green ready this is reality reality is like well I'm going to go up for a little bit meeting your prediction and then it goes you know and it's a smooth tailing off to the end but this is real that's what's actually happened that's the intensity as a function of frequency and that is a big difference over here at high frequencies now a lot of people like to do these in terms of wavelength so I think I should show that also I'll show intensity as a function of wavelength and that graph looks like this that the high the high wavelength is a low intensity so I'm going to start my wrong graph over here and the ultraviolet catastrophe says that as wavelength approaches zero the amount of energy we've got coming out of the blackbody is infinity that's kind of nasty but what actually happens in seafoam green is we're tracing this line along for a little bit and then it goes shoo and then at a higher temperature ooh oh maybe I should emphasize this a little bit more if you look at a blackbody or even any particular thing that's not particularly reflective if you look at that thing oh wait if you look at something in perfect darkness and it is only the only light coming from it is light that comes from its own temperature I don't want any sort of chemical generation of light or anything this would be a low temperature as we raise the temperature the color changes so I'm saying that as far as blackbody radiation the only thing that affects the color of a thing is its temperature color is proportional to temperature and proportional might be a little bit sloppy of a thing to say and that goes like that this is a higher temperature and this is a really high temperature and it goes down and the cool thing is that the science that's going to result from this is going to be called quantum mechanics and quantum mechanics addresses the ultraviolet catastrophe and keeps these guys from exploding but you have to recognize that this is a problem also I want to point out that this peak wavelength here is given by Wiens displacement law this peak wavelength or we could talk about the peak frequency here for this real case right here this is the frequency at the peak and I'm just going to say that the frequency of the peak intensity is in fact some stupid constant it's some number times the temperature Wien said that pretty good idea right very very interesting if you have a higher temperature then you're going to peak at a higher frequency correspondingly if you have a higher temperature then your peak wavelength will be smaller which is a higher energy bit of light so I think I want to leave it right there and then tell you how plunk managed to solve this enormous problem in physics and some of the consequences of his decisions get behind

Channel: Doc Schuster

Views: 127,595

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Keywords: solve, tutor, WGHS, understand, help, problem, science, AP

Id: GgD3Um_f0DQ

Length: 11min 26sec (686 seconds)

Published: Thu Apr 04 2013