What determines frequency of oscillator in black body?

[nonequilibrium]

Hello,

If I understand correctly, the main contribution inside solids that result in the behavior of a black body at high temperatures is that the electron clouds vibrate around their nuclei. Please correct me if I'm wrong.

If I'm correct: to get a black body spectrum every frequency should be possible (or anyway, a lot of them should be, not just a handful of frequencies, I mean) and I was wondering how exactly the frequencies are physically determined. I assume you cannot model every atom as isolated? (because then you would get the same frequency for every atom, assuming your solid is homogeneous, and a quick derivation based on a simple model where the electron cloud is assumed homogeneous, leads me to $\omega = \frac{q}{\sqrt{4 \pi m \epsilon_0 R^3}}$ where q is the absolute charge of the cloud, and if we assume that "volume ~ #particles" then $\omega \propto \sqrt{N}$ where N are the number of electrons). So is it the vast interconnection of the atoms that lead to the variation of frequencies needed for black body radiation? So is it correct that a gas of hot atoms (but no plasma!) cannot exhibit black body radiation? And is it complex to actually calculate the frequencies?

Thank you.

 

[Drakkith]

I'm not sure we can realistically explain a perfect black body, as there isn't one. To my knowledge it is the electrons moving up and down energy levels that emits light, as well as moving around the material as a whole in the case of a conductor. But does a conductor have a more continuous spectrum than other materials? That I don't know.

As for a gas, I don't believe it can as the atoms are not bound together in large amounts. Many nebula emit light in very specific wavelengths that relates to the type of gas that is being excited, but not over the whole spectrum, which leads me to believe that it cannot obey the rules for black body radiation.

 

[nonequilibrium]

Hello Drakkith, thanks for the reply.

I'm not sure we can realistically explain a perfect black body, as there isn't one

I don't think such an objection is justified. What I'm asking about is necessary to understand why the idealization would work, i.e. how physical solids radiate at many different kinds of frequencies so that the mathematical model of a black body is justified.

To my knowledge it is the electrons moving up and down energy levels that emits light, as well as moving around the material as a whole in the case of a conductor.

Do you have any sources that say the electrons hopping between atomic energy lines are a significant contribution to a black body spectrum?
Free electrons might contribute to the black body spectrum, but anyway the black body spectrum is not restricted to conductors, so that can't be it.
I think the oscillation of the electron cloud relative to the nucleus is the most convincing contribution I've heard of so far, but I have yet to figure out how the fact that the atoms are thightly bound comes into play in determining a wide variety of possible frequencies.

Many nebula emit light in very specific wavelengths that relates to the type of gas that is being excited, but not over the whole spectrum, which leads me to believe that it cannot obey the rules for black body radiation.

Yeah, that reasoning would indeed be conclusive if nebulae were hot enough for solids to normally exhibit black body radiation. I'm not implying that they're not, but I am saying that I have no idea.

 

[Drakkith]

Hello Drakkith, thanks for the reply.


I don't think such an objection is justified. What I'm asking about is necessary to understand why the idealization would work, i.e. how physical solids radiate at many different kinds of frequencies so that the mathematical model of a black body is justified.

It's not really an objection, it's just that the situation is complicated, but I do see your point.

Do you have any sources that say the electrons hopping between atomic energy lines are a significant contribution to a black body spectrum?
Free electrons might contribute to the black body spectrum, but anyway the black body spectrum is not restricted to conductors, so that can't be it.
I think the oscillation of the electron cloud relative to the nucleus is the most convincing contribution I've heard of so far, but I have yet to figure out how the fact that the atoms are thightly bound comes into play in determining a wide variety of possible frequencies.

I have no sources saying that, but it was my own understanding that led me to believe it. Per wikipedia on thermal radiation: Thermal energy is the collective mean kinetic energy of the random movements of atoms and molecules in matter.

I had thought that electrons moving up and down energy levels would contribute, but now I am unsure.

Yeah, that reasoning would indeed be conclusive if nebulae were hot enough for solids to normally exhibit black body radiation. I'm not implying that they're not, but I am saying that I have no idea.

I'm pretty sure that they are. Much of the light from an emission nebula comes from ultraviolet light ionizing the gas, with the gas then emitting specific wavelengths once the ions bind with electrons again. However I cannot see this happening without the conditions in the nebula also being very hot from the rest of the radiation emitted by the stars inside the nebula.

 

[fluidistic]

I don't think that the electrons changing atomic energy levels are responsible for the black body radiation. Otherwise the spectrum would be discret (see emission lines: http://en.wikipedia.org/wiki/File:Spectral_lines_en.PNG).
Good question, I'm currently studying a modern physics course and would like to know the answer to your original question.
I asked a similar question not so long ago, what's the difference between the emission of a material in a flame test and the emission of a black body and why the material in the flame test doesn't behave like a black body nor a gray body.

 

[cacosomoza]

I'd like to recover the initial question: is it the case that black body spectrum is made up from an infinity of contributions of quantum transitions (electron, rotational modes, etc) which sum up to a continuous distribution? How complex should the chemical ingredients of the boundaries should be so that such a continuity is obtained? I've seen carbon based materials such as graphite which show spectrums similar to those of black body radiation. How stuff can be black with a single atom species? Is it graphite spectrum that rich?

I have the feeling I'm missing the big picture about colour, thermal radiation equilibrium, and so on. Somebody could help?

 

[Drakkith]

I THINK that in a solid material the charged particles can have almost any amount of thermal energy, and since vibation, rotation, and etc of the particles is what thermal energy is, then the possible spectrum emitted from anyone particle is nearly infinite. If an electron can be imparted with anywhere from 0.001 ev to 100 ev+ then its emitted radiation when it is slowed down is also nearly infinite. The higher the temperature of the material the more often an electron or other particle is kicked with the higher ev's.

 

[fluidistic]

I'd like to recover the initial question: is it the case that black body spectrum is made up from an infinity of contributions of quantum transitions (electron, rotational modes, etc) which sum up to a continuous distribution? How complex should the chemical ingredients of the boundaries should be so that such a continuity is obtained? I've seen carbon based materials such as graphite which show spectrums similar to those of black body radiation. How stuff can be black with a single atom species? Is it graphite spectrum that rich?

I have the feeling I'm missing the big picture about colour, thermal radiation equilibrium, and so on. Somebody could help?

I don't think graphite is any special regarding the black body radiation. I know that metals have usually a high emissivity, hence they behave somehow closely as a black body.

 

[cacosomoza]

Ok, my conclusion is that I should dissolve my "photon equals electron jump" dogma and wait and study the optical properties of materials. Anyway, I liked what Drakkith said about the mechanical nature of thermal energy (vibrational modes, rotation, translation too?) I find extremely hard to link atom spectra with accelerating charge radiation, and I usually tend to think exclusively on the first when thinking of light.Anyway, thanks, if you guys find any good website (I already checked wikipedia) with a wonderful review of Black body radiation, I would appreciate that.