Black Body Radiation -- why is it not at discrete wavelengths?

Main Question or Discussion Point

I was looking at Kirchoffs Laws:
"A solid, liquid or dense gas produces a continuous spectrum".

I would expect objects to produce an emission spectrum since we would be observing the photons that come from spontaneous emission of electrons in excited states. This photons are specific to the energy transition levels and thus the idea of a continuous spectrum is not clear to me. How can a pure hydrogen star let say have a continuous spectrum if its atoms are only hydrogen atoms and thus its photos should be bould to a particular frequency.
If I take into account recombination or stimulated emission, would that take care of 'generating' the continuous spectrum ?
 

Answers and Replies

phyzguy
Science Advisor
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If you take your example of a hydrogen star, there are more ways to emit radiation than just atomic transitions. For example, there are free electrons, and when they scatter off of the heavier nuclei, they are accelerated and emit radiation through bremsstrahlung, which is a continuous spectrum. Also, even the radiation from atomic transitions doesn't just freely propagate out of the star. It can scatter off atoms and free charged particles, and this shifts the frequency. It's best to think of the star as a "soup" of photons, atoms and charged particles all scattering off each other. This thermalizes the photons, so you get a black-body spectrum.
 
Nugatory
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since we would be observing the photons that come from spontaneous emission of electrons in excited states.
Those transitions are not the source of the radiation we're observing. Any chunk of matter dense enough to be emitting thermal radiation is made up of an enormous number of charged particles (postive-charged nuclei, bound and unbound negative-charged electrons) moving in a very complicated electromagnetic fields as they interact with one another in complicated and random ways.

One the other hand, the calculations that give us discrete frequencies from individual bound electrons changing energy levels come from considering an isolated atom, one in which all interactions except between the electron and the nucleus can be ignored. That's a useful and important model in many problems, but it's not especially relevant to blackbody radiation.
 
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Sebastian, your question is a very good one.

When we think of a blackbody we are thinking of an idealized model. You are right to think that the emission spectrum will affect what we see. In fact the radiant spectrum we measure from an object (ignoring any absorption from an intervening gas) will be the (ideal) blackbody spectrum convoluted with (multiplied by) its emissivity spectrum (which is related to absorption). This means that we will not be able to measure a perfect blackbody spectrum.

As was said by others above, a star of pure hydrogen would not be a dilute hydrogen gas. It is a plasma. It will have free electrons, ionized hydrogen and atomic hydrogen at various densities. All of which have various emissivity spectra. In addition there will be a gas of hydrogen that absorbs some of the spectrum from the 'surface' of the star.
 

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