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Chemistry: The Ultraviolet Catastrophe

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  • Type: Video Tutorial
  • Length: 13:30
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 145 MB
  • Posted: 07/14/2009

This lesson is part of the following series:

Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Modern Atomic Theory (13 lessons, $21.78)
Chemistry: Electromagnetic Radiation, Quantum (7 lessons, $12.87)

This lesson was selected from a broader, comprehensive course, Chemistry, taught by Professor Harman, Professor Yee, and Professor Sammakia. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidation-reduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more.

Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electron-rich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.

Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies molecule-based magnetism.

Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.

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Thinkwell
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We're all familiar with an electric burner like one would have on a stove. What's happening here is simply that electricity is being passed through a filament, the filament, because it's resistive, heats up, and it reaches a sufficient temperature that it starts to glow, starts to give off, in other words, visible light. Now, we also know that if we increase the temperature by running more electricity through it that not only does it seem brighter to us, but the actual color is changes. Maybe it shifts from a reddish color to a more orangish color as we go to a higher temperature. This is a phenomenon referred to as incandescence, the giving off of visible radiation from a hot body. Also, physicists call it "black body radiation," the idea that no matter what the material is, if it's at a sufficient temperature then we get this emission of different frequencies of light.
Another place that we will see it is that we're very familiar with would be an incandescent light bulb. Now, the idea here is exactly the same, actually. We're going to pass electricity through a filament. This is a tungsten filament. Again, it's resistive so it heats up. It heats up to a temperature that would get visible radiation from it. Now, you'll notice that the color is very different than the color that we get off of the stove, off of the burner, and that's simply because the temperature is different. This is a higher temperature, so we see different--our eyes perceive a different color than from the lower temperature.
Now, remember that we know that white light is actually a mixture of many different frequencies of light, so we can imagine taking that light, passing it through, let's say, a prism, which allows us to separate out all of the different frequencies of white light. We could analyze the frequencies as a function of how much of those different frequencies we get. If we do that we get a curve, a curve for black body radiation. And I want to focus your attention on the blue curve here. Now, let's take a look at this. This is a lot to stare at here. This is wavelength of the light. Again, remember, wavelength is inversely proportional to frequencies. Now, here we have long wavelength going to short wavelength, so we're low frequency going to high frequency, and you'll notice that as we go to higher and higher frequencies, that the amount of light that we get increases. We get a higher intensity as to go to higher frequency through this period of a curve--this portion of the curve here.
Now, notice what else happens. We reach a peak. This peak would correspond to the frequency that is the greatest intensity that we get out at a particular temperature. Now just to clarify here, this curve is only for one temperature. And then the intensity starts to drop off. So as we go to higher frequency light, the intensity becomes less. Now that's just the data. That's just the type of frequencies that come out of, let's say, a light bulb filament.
Okay, now. Remember we said that that will change as a function of temperature. So if I look at another curve, but at a different temperature than that, let's say it's a higher temperature, then what will happen is this peak will broaden out at a higher temperature, and it will start to shift so that the maximum, the peak here, actually moves to higher frequency.
So again, our eye perceives a color change as that process happens. You see something going from a red color to more of an orange color, to ultimately a white color. We're getting full visible spectrum. So the interesting question is, why does this happen? Why do we get frequencies of different intensities when we heat up a body to very high temperatures?
To do that we're going to do what scientists often do. We're going to think of a model, something that helps us understand what's actually going on in the solid. Now, imagine that this is a block of metal and in that metal was have a lot of nuclei--I'll say it's a chunk of iron, a lot of different iron nuclei--connected together by electrons. Now, we can think of this as a bunch of balls connected together by a spring. The important piece here is that the electrons don't hold those atoms in fixed position, but allow a certain amount of vibration to occur. So imagine all of these things at a certain temperature wiggling. Now also add to that the idea that as we increase temperature we're putting more energy into this system, so everything wiggles with more emotion, if you will, greater amplitude than all of these vibrations. What does that have to do with light?
Okay. Let's think of a simpler case for a moment. Think of just two atoms connected by a spring and allow those atoms to be vibrating against each other with a certain frequency. Since these two atoms are vibrating, it sets up an oscillating electric and magnetic field. Well, that's essentially what light is, so as you have these two atoms oscillating against each other you, in a sense, are creating a wave of light. Now, depending on the frequency of this vibration you'll get a different frequency of light. So something this simple will have only one frequency, but a system like this, where you have a block of iron again, you have many different possible frequencies that are available, a really slow frequency will give you a low frequency light. A very high frequency vibration will give you a high frequency light, and so you get an entire spectrum of different frequencies of light because this very complex system can vibrate in a number of different ways. In the language of physics there are many different oscillators with different frequencies in this block of iron, so we get a number of different frequencies of light emitted from the block of iron. As we put energy into it, we get everything vibrating.
Now, that's all fine and dandy. That gives us a nice qualitative explanation for why we get white light coming out of a very hot body. But it doesn't explain everything, and I'll tell you the problem. If we do a bunch of calculations, and thank goodness we're not going to do that--you have to trust me on this--what we conclude is that the number of oscillators at high frequency in a block of iron greatly outnumber the number of oscillators with a low frequency.
Now what that means is that we expect to see, as we go to higher frequency, since there are more oscillators at high frequency we expect to see more light being emitted at high frequency. Well, that works just great through this part of the curve, and in fact, this red line shows what the calculation predicts based on this model. Based on this model we expect to see higher and higher frequencies, more and more light emitted, because I have a greater number of oscillators. But look at the difference. They match pretty well here.
Look at this huge problem as we get into the higher frequencies. Whereas the prediction is that we should get more and more intensity from high frequencies, and in particular, let's say, the ultraviolet range, we should have huge amounts of ultraviolet radiation if we're at this temperature, whatever our temperature is. But in practice, experimental data says that we peak and we drop back down again. This is a tremendous problem for the physicist back at the turn of the century because our calculation is based on simple ideas of nuclei with defined masses being held together by electrons, with defined attractions, predicts this, and the data shows us that it's very, very different than that. In fact, this is termed "the ultraviolet catastrophe," because there is not sufficient amounts of ultraviolet radiation given off at a given temperature, much less than what's predicted, and so the catastrophe is that it just doesn't fit our idea of a classical world, the idea that we can treat atoms and molecules as defined nuclei with electrons holding them together. It falls apart. There's just no way that we can explain this data based on that old idea, or I should say that incomplete idea.
So this was the problem plaguing physicists at the turn of the century. Now, Planck, Max Planck, in 1900, came up with a brilliant idea, a brilliant postulate. He suggested that perhaps it's not possible to put in any arbitrary amount of energy into an oscillator, but you have to put in a defined amount of energy. Now, what am I talking about? Remember our notion that you could take water and you could pour water into a cup and have seemingly any volume of water you want, any mass of water that you want. But if we really think about it, that's not entirely true. We can have one molecule, two molecules, three molecules, 50,000 molecules, but you can't have one-and-a-half molecules. The mass of water, the mass of anything is quantized.
Well, what if the same idea is true for energy? The idea that we have a vibration with a certain amount of energy in this oscillator, and we want to put more energy into the oscillator to make it vibrate with a greater amplitude. But what Planck is suggesting is maybe that's not true. Maybe you can't have any arbitrary amount of energy in there. Maybe you have to add the energy in defined packets, defined quanta of energy. Now, mathematically expresses that idea the following way. The energy in an oscillator is proportional to the frequency of the oscillator times some constant, which later became known as Planck's constant, bearing his name, times an integer, where that integer is an integer--it can be one, two, three. That provides this quantum quantization of energy. So the idea is that an oscillator can have one unit of energy, in other words, H-nu, two units of energy, 2H-nu, 3H-nu and so on, but nothing in between.
Now, this is a very tough idea, but if you accept that--and there's no good reason to accept that except that it explains the data. If you add this provision that the energy in an oscillator is quantized and we go back then to our idea of a block of iron and say that, "Okay, you've got a bunch of different oscillators with different frequencies, but the high frequency oscillator must take their packets of energy as a big chunk of energy each time, whereas the low frequency oscillators only need a little energy at a time, what that implies then is that the high frequency oscillators don't, on average, get as much of the energy in the block of iron, and more of the lower frequency oscillators do.
All this means is that you get a lot more vibrations that are low frequency than high frequency, and therefore, returning now to our curve once again, with that provision that we have quantized energy in these oscillations, we end up perfectly describing this peak, matching reality.
Now, it's said that Planck, throughout his entire life, never really believed this idea, the idea that energy was quantized somehow was so foreign, especially back in 1900, that it's very hard to accept. But nonetheless, it was the only way we could answer the question of how we get this type of unusual behavior as far as intensity of light as a function of frequency for a given temperature. So it described the data and it was a huge sign, a warning sign to physicists and chemists at the time that something dramatic had to happen as far as the way we thought about our physical world. There had to be a paradigm shift, a different way of thinking about the world, and this notion that energy in an oscillator had to be quantized, was one of several key ideas that had to be in place before we could understand physics in a new language.
Modern Atomic Theory
Electromagnetic Radiation and the Idea of Quantum
The Ultraviolet Catastophe Page [3 of 3]

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