How Maxwell's theory of radiation could not explain atomic spectra?

Hydr0matic

No, I've changed my mind somewhat [:)]. Discussing this with you made me realize my assumption about f₀ was, perhaps, a bit unrealistic. I searched google for anything related to "speed, gas, molecules", and I found something called "Maxwell-Boltzmann distribution" - which, much to my surprise, was exactly what I was looking for!

http://www.chem.uidaho.edu/~honors/boltz.html

Reading a bit about M-B distribution has made me even more convinced that I'm on to something. Doesn't the MB curve resemble the Planck curve extremely well ? Except for the fact that the MB curve is normalized, they're basically the same curve ! [8)]
Compare:
http://www.phys.virginia.edu/classes...s/img00001.gif
http://www.chem.uidaho.edu/~honors/boltz2.jpg

I believe the oven concept was originally developed by Rayleigh and Jeans, right ?

Well, instead of trying to invent some equally abstract model based only on the assumptions of two individuals, we should construct a model based on reality and whatever clues can be found in our universe. Because, although the blackbody is just a concept, blackbody radiation is very much real. In fact, everything around us (above 0 K) radiates blackbody radiation, AKA thermal radiation - everything from the rubber under my feet to the hair on my head. So what does one have in common with the other ? Not much, except that they're both made of tiny vibrating particles.

What else can we say about BB radiation ? Well, If we were to compare an object, e.g my coffeecup, with the sun ([:D]), we would undoubtedly consider one to be more of a blackbody than the other - simply because it's closer to meeting the criteria. But why is this ? Basically the only thing they have in common, again, is that they're made of tiny vibrating particles. What really separates the two is the sheer number of particles. This causes the sun's radiation to be completely dominated by BB radiation, while my coffeecup's radiation is completely dominated by discrete atomic spectra. I believe the two are directly related, but that's another chapter.

So, based on some simple observations, my conclusion about how to best represent this abstract thing, is simply with a huge quantity of vibrating particles.
"How can we keep the radiative properties away from the disturbing factors of the outside world?" - We simply eliminate the outside world. If all that existed in our universe were tiny vibrating particles, like during billions of years ago close to the big bang, we would have a perfect blackbody - A REAL ONE. If I'm not mistaken, the radiation from this blackbody goes by the name of "Cosmic Microwave Background Radiation".

Ok, this is one version of the story. My understanding of what happend is less flattering for Planck. Rayleigh and Jeans were first to publish the blackbody oven model with their Rayleigh-Jeans Law, which led to the famous expression "the ultraviolet catastrophe". Planck, as the brilliant mathematician he was, instantly knew what had to be done in order to make the formula work, and so he did - without any intention of "inventing the quantum". The part about quantization is an interpretation of Planck's formula made afterwards. There is no quantization in Planck's formula, only a limitation on energy per mode. By assuming energies were quantized, one could explain why higher energies were less likely to be emitted. However, contrary to what people seem to believe, this interpretation was not accepted by Planck.

Now that I've found out about Maxwell-Boltzmann distribution I completely understand why Planck's suggestion worked. If we just use an ideal gas as representation for the blackbody instead of an oven, there is no need to assume quantization in order to explain the distribution.

What say you ? Am I at least beginning to make more sense ? [:D]

Thnx again for responding to my posts.

selfAdjoint

You're absolutely right that the Maxwell-Boltzman distribution was used by Planck. The oscillators in Plack's version were to be in thermal equilibrium, so their energies would follow that distibution. And the path from that to the radiation distribution, while not as trivial as you make it seem, was straightforward.

Planck was not a great mathematician, he was a great physicist. And the replacement of the material in the cavity walls with oscillators was a physical idea, not a mathematical one. If you focus on the cavity being able to maintain thermodynamic equilibrium over a period of time, which your cloud could not because of radiation will show you why the cavity is superior. Every bit of radiation produced in one part of the wall of the cavity is absorbed in some other part of the wall. Has to be, by geometry, no place else to go. So absorption = radiation over time, producing a stable distribution for the radiation.

Hydr0matic

A very good article about this subject:
http://physicsweb.org/article/world/13/12/8

And where does the radiation go if the "cloud" covers the entire universe ?

The energy could still make it's way out through the walls, right ?

The cavity is not superior [6)]