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

[Brain]

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?

 

[Integral]

Could you rephrase that post. I simply cannot understand what you are trying to say.

 

[mathman]

I'm not familiar with Maxwell's theory. However, it takes quantum mechanics (developed long after Maxwell) to explain atomic spectra.

 

[Kube]

I think you might be referring to Einstein's Photoelectric effect. I don't really remember much about it, but check it out anyways.

 

[quartodeciman]

One problem arises immediately from the Rutherford planetary model of atoms. If electrons whiz in orbits around a positively-charged nucleus, why don't they continuously radiate away their energy? Since many atoms are quite stable, this evidently isn't happening. On the other hand, matter made of atoms can be made to emit radiation, without destablizing them electrically. How can Maxwell theory account for this?

 

[Brain]

Why can Mexwell's theory of radiationo not explain atomic spectra?

Why Maxwell's theory of radiation can't explain atomic spectra?

 

[1100f]

Originally posted by Brain
Why Maxwell's theory of radiation can't 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 spectrum

 

[Hydr0matic]

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

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.

 

[selfAdjoint]

Well it would have to explain the discrete spectrum (separate lines) of the elements, and their numerical relationships like the Balmer series. Maxwell's theory doesn't have this kind of stuff inside it. The great early achievement for Bohr's old quantum theory was to account for the spectrum of hydrogen. Existing (Maxwell) theory couldn't do it.

And there is the famous story of the ultra-violet catastrophe. Theories of the distribution of energy by frequency in black body radiation, based on Maxwell, predicted that most of the energy would be concentrated at the highest frequencies. But experiment showed the energy was distributed along a kind of warped bell curve, with a peak energy at some frequency and lower energies on either side. Planck realized that the problem with the theories was that they assummed energy (actually action) could be infinitely subdivided. By assuming the contrary that there was a minimum action, he was able to derive the correct law. His minimum amount of action is now called Planck's constant.

 

[Hydr0matic]

Yes, I know the whole story

I wouldn't have said what I said if I wasn't just starting a new thread about it in the Theory development forum. As you seem to know the details of the story as well, I would really appreciate a comment from you. ... please ?

I skipped the part about atomic spectra though, so the thread wouldn't be too long. If would want to hear about it let me know..

https://www.physicsforums.com/showthread.php?s=&threadid=12213

 

[selfAdjoint]

HydrOmatic, I think this is the core of your ides:

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 !

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?

 

[Njorl]

Originally posted by Brain
Why Maxwell's theory of radiation can't explain atomic spectra?

For the same reason my blender does not make coffee.

Njorl

 

[Hydr0matic]

Originally 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?

Thnx for your response

I say you are correct. A single oscillator itself produces the entire blackbody spectrum, but you can only see it if you cover every angle. But since we're only observing the oscillators from a single angle, we need multiple oscillators (randomly oriented) to get the full spectrum.

What was it that you didn't see ? I'm confused because you seem to disagree with something I said, yet your argument is in line with what I'm saying.

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).

 

[selfAdjoint]

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).

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?

 

[Hydr0matic]

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?

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 .

Because of the thermal equilibrium the chance of an oscillator emitting f_max and f_min "flat on to us" is very slim. The more the frequency deviates from f₀, the less likely it is to be emitted "flat on".

Am I mistaking ? I didn't consider this a too unrealistic assumption. Maybe I was wrong ?

 

[Hydr0matic]

Do you see it ? .. Want to hear about how atomic spectra fits into this ?

 

[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. Well good luck with the distribution. You have to get the fourth power dependence on absolute temperature. Planck did, with his oven.

BTW, you keep knocking the oven. The original concept was the "black body" which was a perfect emitter and an equally perfect absorber. And its emissions would be dependent on its temperature. This is the concept that comes from Clausius.

The the question is, how can we represent this abstract thing correctly? How can we keep the radiative properties away from the disturbing factors of the outside world? And the oven was the answer. Actually it is called a thermal cavity. It's deep in the interior of a solid body, so it will come to thermal equilibrium undisturbed. Then once it's at thermal equilibrium, emission and absorption are by definition equal, so the property of the black body is achieved. AND THIS IS INDEPENDENT OF THE MATERIAL USED. So long as it can radiate.

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.

 

[Hydr0matic]

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.

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 !
Compare:
http://www.phys.virginia.edu/classes/252/bbr_images/img00001.gif
http://www.chem.uidaho.edu/~honors/boltz2.jpg

Planck did, with his oven.

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

The the question is, how can we represent this abstract thing correctly?

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 ( ), 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".

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.

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.

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 ?

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

which your cloud could not because of radiation

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

no place else to go

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

The cavity is not superior