Quantization of Energy Part 1: Blackbody Radiation and the Ultraviolet Catastrophe


Hey it’s professor Dave, let’s talk about the ultraviolet catastrophe. We know that the classical physics of Newton and pals reigned supreme for a few centuries, so what were the events that finally exposed its limitations? What was the first thing that suggested there was more to the universe than we had previously thought? This seismic shift was initiated in 1901 when Max Planck solved something called the ultraviolet catastrophe. The problem went like this. Certain objects are called blackbodies because they emit electromagnetic radiation of all wavelengths. The sun is an example of such an object, and we can take a look at the distribution of the wavelengths of light that we receive from the sun. Most of it is in the visible spectrum, which is why our eyesight evolved to pick up this kind of light, but we also receive light on either side, in the UV portion as well as infrared and beyond. A hot piece of metal will also do this, and this was the way we studied blackbodies at the time, noting that the distribution depends not at all on the material but only on temperature, with the particular wavelength that is emitted with maximum intensity shifting left as temperature increases. This maximum will move into the visible spectrum at around 4000 Kelvin and above. This is why very hot objects appear to glow, like a hot oven, light bulb filament, or the sun and other stars, because objects at these temperatures emit a lot of visible light, as opposed to something like the human body, which at around 310 Kelvin, emits essentially no visible light, which is why we can’t see each other in the dark. The problem with the blackbody spectrum was that classical electromagnetism could not account for it. Mathematical models attempting to produce these distributions were able to fit the data for the longer wavelengths, but they did not predict that the intensity would dip down to the left for the UV portion of the spectrum as experimental data Illustrated. Instead, the math predicted that the intensity would continue to increase as the wavelength decreased, and become infinitely large as the wavelength approached zero. Of course, we know that this can’t be true, otherwise every time you use the oven you would get blasted with UV radiation. This contradiction was dubbed, somewhat dramatically, the ultraviolet catastrophe. In science, if a theory does not accurately align with observations of reality, it must be revised, and so we realized that classical electromagnetism, as powerful as it is, must have some kind of limitations in its ability to describe light and energy. As we said, Max Planck solved this problem, and he did so by introducing a concept called quantization. We know from classical physics that heat is just the transfer of kinetic energy from one place to another. In the case of a piece of solid hot metal, that kinetic energy takes the form of atomic vibrations or oscillations. These vibrations are what generate the light we see in the blackbody spectrum. Planck proposed that the vibrational energies of these atoms and by extension the energies of the electromagnetic waves emitted by these atoms must be quantized, meaning that rather than being able to take on any value from a continuous series, they can only possess specific discrete values from a set of accepted values. In this way he developed this expression for blackbody radiation, where energy is equal to n, which can be any integer, times h, a term we call Planck’s constant equal to 6.626 times 10^-34 joules seconds, times f, the frequency of radiation. The n value is what results in quantization, as it can only be an integer, and not any fraction or decimal in between, meaning that the resulting energies will also comprise a set of allowed values, with anything in between being forbidden. This application of quantization and the accompanying Planck’s constant were developed in ad hoc manner, meaning that they were simply proposed for practical purposes, but they allowed for the accurate prediction of the true distribution of blackbody radiation at all wavelengths, which meant that this constant was more than a mathematical fluke, but a clue as to the fundamental nature of reality, and the fact that Planck’s constant is so incredibly small explains why the notion of quantization of energy had not cropped up before, because it shows that energy is quantized on such an incredibly small scale that the gradations between the allowed values are utterly miniscule so as to appear non-existent to any measuring apparatus. Energy appears to be continuous to macroscopic beings such as humans but on the fundamental level it is indeed quantized, even though this conclusion was so strange that most scientists of the time, including Planck, couldn’t believe that it had actual concrete physical meaning. This was the first time that quantization had solved such a big problem in physics, but it wouldn’t be the last. It was the first in a series of developments that would utterly transform the field of physics, and by extension, our perception of reality. While Planck’s work solved one problem it created another. Why is there quantization of energy? This marked the beginning of the quantum revolution, so let’s continue and see what happened next. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so I can keep making content, and as always feel free to email me:

100 Comments

  1. Nice explanation. I am a physics lay person. I have never heard that explanation of Planck’s constant before, it suddenly seems to me to have fundamental importance.

  2. I am currently in the last leg of my schooling to become an x-ray tech; these videos have helped me understand the more drawn out parts of radiation physics than any book that I have paid hundreds of dollars for. thank you so much!! and please keep making these videos

  3. Are you sure the light emitted by a hot backbody is caused by atomic vibrations? Isn't it due to electrons continuously jumping to higher energy orbitals and falling down again?

  4. Professor Dave, the atomic vibration was the explanation back in 1900ish when they didn't know anything about the electronic transitions!

  5. Hi sorry my question is probably stupid, but why was it not called x-ray catastrophe? Because the way I see it, with classical physics, the wavelength will carry on reducing further than uv as the temperature goes up. So why not 'x-ray' or even 'gamma ray' catastrophe?

  6. Hi. I want to ask about ultraviolet catastrophe. The ultraviolet catastrophe came from the Rayleigh- Jeans 's formula. I want to know that did any scientists also study about ultraviolet and they were also wrong like Rayleigh- Jeans? (I also know Wien's distribution law) . Sorry for my English. If anyone knows, please tell me. Thank you so much

  7. The problem starts with the interpretation of this mathematics, and mistaking it for reality. The numbers you see here are derived from MEASUREMENTS, and measurements always have a THRESHOLD, which discards part of the energy. This threshold, in regard to electromagnetic waves, is due to the fact all detectors are made of matter, and the deficit in detected spectrum does not tell us about the nature of light, but means MATTER does not REACT with a lot of electromagnetic waves, but only with part of them, as described by Planck. So the electromagnetic waves are continuous, and follow Einstein equations, but interact with matter only partially. Imagine you have a fence net dipped in water. Only a small part of the fence net will react to the incoming water waves, despite the fence being "a single object". That is how matter looks like – it has a selective response to electromagnetic radiation. So don't let anyone tell you Quantum Electrodynamics describes THE WORLD – it only describes the KNOWLEDGE about DETECTABLE PART of the world. It is perfectly allowed to have waves of different wavelengths, but they are very hard to create, because matter is "tuned" to the Planck frequencies, and similarly very hard to detect. The world of matter is much more like a fine net, full of empty space, which has a rigid resonant frequencies. And the detection is always only through resonance.

  8. Oven doesn't have high temperatures…
    So i didn't get you at this…

    Classical Mechanics is false because we aren't blasted with Ultra Violet rays

  9. How taking energy as packets called quantum will solve the problem
    What if it absorbs continously

  10. Does scientists understand why it is quantized and why only certain orbits are allowed around atoms? (The Planck and Bohr propositions)To me quantization looks like a filtering mechanism. Our universe gets certain integer values while the remainders is not observed by our senses or monitoring devices.If atoms are made of quarks, then protons/electrons and other macro building blocks seems to be beat frequencies of higher order frequencies. Just like DNA only has ACGT we only get certain allowed frequencies alloted to our universe. The question is where does the fine tuning come from? Perhaps not a physics problem, but nonetheless.The code must then be observer code corresponding to observable code. Radio and transmitter in tune.

  11. Planck have his fuction and was it Rydberg with his own to describe emittance at different scale / temperature range. Obviously Einstein formulate general function 1905 to be correct at all temperatures as a side study of his famous photo electric postulation. Higher the temperature then higher and narrower the peak freguency is and increasing and decaying exponentially.

  12. Do you mean result is independent to the material used in the experiment but only depends on temperature? Or I miss something. Good day.

  13. This video was awesome, and helped me so much. But I still do not understand where Planck obtained the constant from, can anyone explain?

  14. It's absolutely incredible that an ad hoc utilization of Planck's expression for black body radiation turned out to be so amazingly useful. It's hard to believe sometimes that hypotheses can become such hard & fast truths about spacetime. Wow.
    And sometimes it feels like it comes from simple laziness:
    "I just want to deal with integers right now; it's easier. Oh, that reveals fundamental truths about the nature of reality? That's cool, I guess. 😎" -Max Planck, probably

  15. It only makes sense that when the wave length is approaching zero the energy pulls towards infinite. After all , energy is just an infinite field of possibilities , isn't it ?
    Anything infinite in nature, in order to become part of our limit based reality must become limited. That can be done only by conventions, by setting theoretical limits .
    When an infinite field of possibilities is limited to 1 , the probability becomes 1 and we call it real .
    We do that with energy – how else could we get a quanta ? – with space, with time – only by conventions we can get from an infinite and perpetual now to time intervals and past / present / future .
    In this case the limitations are set by Planks constant. Not the first and not the last time when we need to put in place a "constant" in order for the theory to make sense, is it ?

  16. argument from ignorance logical fallacy. Using this same logic you can use popcorn to prove that energy is quantizes – you just have to ignore all the other possibilities (like the phonon work of Owen Richardson and thermionic radiation which directly contradicts the concept quantized energy).

  17. I heard somewhere that Planck just got irritated with the math and introduced h as the minimum energy value, fully certain that h=0, so that classical mechanics would still work and minimum energy would still be 0. But later in the calculation he saw that h has an actual value, and not just 0

  18. 0:39 absorb not emit ,just think about it whan u shine battery light at black ball it absorbs em radiation of all wl.(avalible) not emits. To be clear bb : absorbs em radiation of all wl. and CAN emit em rad. of all wl. .

  19. My question is, the sun gives off UVR, under classical is supposed to give off only UV radiation and no other spectrum? Does classical physics fail because we do not have a perfect black-body to experiment with?

  20. If the whole world had teachers like you, and scientists like Einstein still alive, we would surely have colonized Mars till now.

  21. "catastrophe" comes from the Greek and means, literally, nothing more than "turning downwards", not a "dramatic turn of events". "ultraviolet catastrophe" describes the dipping down in the uv spectrum.

  22. Dave I believe the key to making a math connection between capacitance and wavelength or frequency of light is through Planck constant
    The math requires a full understanding of capacitance via parallel plates and the analogy of quanta units of energy. The math shows that h or the constant is related to permittivity and permeability and fits into E=Hf in the end. Thanks

  23. How is sun a blackbody? A black body neither reflects nor transmits any incident radiation and therefore appears black.

  24. Wait, wait. First, I love your channel, but you said (of the sun's radiation profile) that "most of it is in the visible spectrum, which is why our eye sight evolved to pick up this kind of light." I take serious issue with this statement as anthropomorphic. We call it the visible spectrum because it's the range that humans eyes evolved to pick up. Other creatures pick up light into what we call "ultra-violet", while others still can see down into what we call "infra-red". Giving it a neutral point of view presentation opens up the pupil's minds (puns intended) to think outside of the human experience. Of course, I take your point on why we most likely evolved our eye sight too. 🙂

    Here's another vision related anthropomorphism. I learned in elementary school that red, green and blue light make white and that you can make any color by mixing the three. The representations that our digital cameras and RGB monitors make look beautiful to us, almost like the real thing, but a mantis shrimp (a.k.a., "thumb splitter") who's eyes detect light peeking at 12 wavelengths (instead of our three) would think we were on drugs or blind, not realizing that it's both. Well, at least they might think that if they had more complex brains and didn't have to fight with HMOs to find a medication that's covered.

    I would love to see a representation of famous paintings imaged with a high resolution spectrographic camera and re-processed to show the approximate color representation of various other animals through their eyes, like the mantis shrimp. Obviously, those cones are receptive at a peek wavelength so when two different cones both get a signal our brain interpolates in between to guess the real color, so by using just red, blue an green, we're tricking our eyes like we're some kind of cyborg.

  25. that makes sense… if you look it everything is just a vibration of sort the reason its quantised is because the separation between level is just the "dead space where force cancel" before it start its unbalance again

  26. Sir please explain what do you mean by we would get blasted by UV radiation every time we use microwave if the results from the classical mechanics were true. I tried studying the working of a microwave and came to know that standing waves are formed inside the oven with wavelength around 6.4 cm. How does this fit in the information you provided in the video?

  27. That is exactly what it is; a "tale" it is not physics just science. The basic laws of physics are still at the base of his discovery.

  28. "Why" indeed. All quantization arises from boundary conditions. Go through derivation of Blackbody-radiation and one quickly sees quantization is not inherent to the light itself, rather the boundary conditions of the thermal conditions that created the light. Similarly with atomic emission of light. It's the boundary condition of the atomic potential well that causes light to be quantized, and is not inherent to light itself. This distinction can be easily proven by a thought-experiment. Hold a positive charged ball in one hand and a negative in the other; then spin at whatever speed you like? (more…)

    The resulting E/M wave created is then a function of the speed, not of any boundary condition. And the speed is continuously variable, not limited by any quantization. Thus, unquantized photons are created.

    Most photons we encounter are quantized (sun, lightbulbs, LED's, fluorescents, etc.), but the fact unquantized photons exist, disproves huge swaths of physics orthodoxy. Because, it's not light that's quantized, rather the boundary conditions quantize photons that most often create that light.

  29. What determines the value of N in Plank's equation?  Since f = c/wavelength, shouldn't energy still approach infinity if wavelength approaches zero

  30. It's the 21st century and I'm still a Newtonian at heart. And an "everything is continuous" kind of guy.

  31. But the question is how did Plank explained the low intensity of the high frequency waves?
    According to his formula,
    E should increase with increase in frequency.
    But beyong visible spectrum , waves with high frequency contains less energy or are of less intensity.

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