# Why is the planck function continuous and not discrete?

If we imagine a object made up of Hydrogen gas that is optically thick to all radiation, and is in thermal equilibrium, then, microscopically, photons will be emitted and absorbed as emission/absorption lines.

However, the overall object should emit radiation according to Planck’s Law, which describes intensity as a continuous function of wavelength (and temperature).

How does this occur and where do the photons we detect at wavelengths between spectral lines of hydrogen come from originally?

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An object made up from a specific single molecule gas? Photons absorbing photons? Of what variable is your non-continous curve a function of? Such uncharged boson numbers (e.g., in the electromagnetic theory, photons) are not conserved btw., so that's no problem. –  Nikolaj K. Dec 6 '12 at 11:09

Hydrogen gas is not a Hydrogen atom. During some atomic collisions one has more complicated systems than just a Hydrogen atom, i.e. they have more complicated emission/absorption spectrums. As well, there is a Doppler broadening of lines that smears sharp lines. But the principal reason is, of course, (temporarily) creating complex many-atomic (and even plasma) configurations with richer spectrum. In a thick object there is sufficient number of such complex systems.

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Another point would probably be that an object made up entirely of hydrogen atoms is not necessarily a black body and hence does not necessarily obey Planck’s law. –  Claudius Dec 6 '12 at 11:25
In that case it cannot be optically thick (i.e., absorb everything). Such is rare gas around some cosmic objects. It demonstrates absorption lines in the spectrum and is transparent "between lines". –  Vladimir Kalitvianski Dec 6 '12 at 11:29
Ah, correct, thank you very much! :-) –  Claudius Dec 6 '12 at 11:30

I think that there is a simple contradiction in the question: either you define your object as a black body that absorbs and emits every wavelength or you talk about spectral lines.

Hydrogen is not a black body. If you imagine it so then don't be surprised if you reach contradictory conclusions.

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