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Brain
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We all know that Maxwell did such a great work for all physicist. BUT, anyone knows that how Maxwell's theory of radiation could not explain atomic spectra?
According to classical Maxwell's theory, an electron orbiting around the nucleus would radiate em waves. the frequency of these em waves would be the frequency of rotation of the electron around the nuclueus. The electron would loose its energy continuously and this would give a continuous spectrumOriginally posted by Brain
Why Maxwell's theory of radiation can't explain atomic spectra?
I consider this a failure of the atomic model, not Maxwell's theory. I don't really see any reason why classical EM theory shouldn't be able to explain atomic spectra.Originally posted by 1100f
According to classical Maxwell's theory, an electron orbiting around the nucleus would radiate em waves. the frequency of these em waves would be the frequency of rotation of the electron around the nuclueus. The electron would loose its energy continuously and this would give a continuous spectrum
The most important difference from a blackbody perspective is the fact that photon intensity doesn't change with the relative angle. The observer will see as many unshifted photons as blueshifted and redshifted. If this was the case in our blackbody, the intensity wouldn't vary as a function of wavelength (As the famous Planck curve). But on the other hand, if the atoms were oscillating charges and the photons were electromagnetic waves, the intensity would vary very much indeed. In fact, Maxwell's equations tells us that the amplitude of an electromagnetic wave is a function of the angle between the oscillation and the radiated wave. This means that the intensity is highest perpendicular to the oscillation, and lowest (zero) in the direction of oscillation. This is why the Planck curve slopes down again at higher frequencies !
Originally posted by Brain
Why Maxwell's theory of radiation can't explain atomic spectra?
Thnx for your responseOriginally posted by selfAdjoint
I don't see this. If you looked at any small area of your radiating gas, you would see waves from oscillators in every orientation, and the angle between them and your line of sight would be all over the map. So it seems to me you would see a UNIFORM field, with all frequencies distibuted the same as for a single oscilator. What do you say?
The important "point" I was making in my post was the fact that the highly dopplershifted waves, ie those at each end of the full spectrum, are radiated when the oscillator is oscillating closely in line with the line of sight, giving them very low intensity. (sloping down the Planck curve at the ends).
Ah, now I understand . The reason is because we're talking about a gas in thermal equilibrium where the oscillators have an average speed and thereby an average oscillation frequency. This is the frequency I named f0 in my post. I get that this is an ideal assumption but so is reflecting EM waves in an oven .Originally posted by selfAdjoint
That's the part I don't see. Why should we only see the extreme frequencies from oscillators in that particular orientation to us? What happens to all the ultra-violet and infrared frequencies produced by oscillators flat on to us?
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!Originally posted by selfAdjoint
So if I understand you, all the oscillators are vibrating at one single frequency f0, but we see different frequencies due to the random orientations of the oscillators and relativistic optics. So the extreme frequencies are relativistically altered versions of f0 and you propose to explain both their existence and their distribution by this mechanism.
I believe the oven concept was originally developed by Rayleigh and Jeans, right ?Planck did, with his oven.
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.The the question is, how can we represent this abstract thing correctly?
Ok, this is one version of the story. My understanding of what happened 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.So Planck was justified by replacing the real material, conceptually, with a gedanken material made out of SHM oscillators with quantized frequencies. He then assumed THEY were in thermal equilibrium which would mean not only were they randomly oriented, but their discrete frequencies folowed a partition function from statistical mechanics appropriate to thermal equilibrium. And that's what Planck used to get his curve.
And where does the radiation go if the "cloud" covers the entire universe ?which your cloud could not because of radiation
The energy could still make it's way out through the walls, right ?no place else to go
Maxwell's theory of radiation, also known as classical electromagnetism, was unable to explain the discrete lines observed in atomic spectra. This is because the theory predicted a continuous spectrum of energy levels, rather than the distinct energy levels that were observed.
Atomic spectra, or the distinct lines of light emitted or absorbed by atoms, provide important clues about the structure and behavior of atoms. The specific wavelengths of light emitted can be used to identify elements and their energy levels, which in turn can reveal information about the arrangement of electrons within the atom.
The inability of Maxwell's theory to explain atomic spectra was a major challenge in the field of physics. This led to the development of quantum mechanics, which introduced the concept of discrete energy levels and explained the behavior of atoms at the subatomic level. Quantum mechanics has since become a fundamental theory in understanding the behavior of matter and energy.
Yes, Maxwell's theory of radiation is still applicable in certain situations, such as in classical optics and electromagnetism. However, it is unable to fully explain the behavior of particles at the atomic and subatomic level, which is where quantum mechanics is needed.
The discovery of atomic spectra challenged traditional ideas about the nature of matter by showing that atoms were not simply indivisible, but rather composed of smaller particles with distinct energy levels. This led to a shift in understanding from a classical, continuous view of matter to a quantum, discrete view.