# What causes a blackbody radiation curve to be continuous?

The ideal blackbody radiation curve (unlike the quantized emission seen from atomic spectra), is continuous over all frequencies. Many objects approximate ideal blackbodies and have radiation curves very similar in shape and continuity to that of an ideal blackbody (often minus some emission and absorption lines from the atoms in an object, such as radiation curves seen from stars). I am wondering what exactly gives rise to a basically continuous blackbody radiation curve in real objects? Since atomic energy states are quantized, it seems real life blackbody curves would have some degree of measurable quantization to them (or perhaps the degree of quantization is so small the radiation curves look continuous).

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perhaps the degree of quantization is so small the radiation curves look continuous

Yes, this is the reason. The correspondence principle says that quantum mechanics has to become classical in the appropriate limit. One way to obtain an appropriate limit is with large numbers of particles. As you increase the number of particles in a material many-body system, you get more and more ways of putting together combinations of states for your material object. The density of states of the object grows very quickly (roughly exponentially) with the number of particles. Therefore the number of possible transitions between states also grows very rapidly.

The number of particles in a tungsten lightbulb filament is something like Avogadro's number. The exponential of Avogadro's number is really, really big.

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Right. and one should remind oneself that even in simple potential problems the energy levels for large n (towards infinity) are really dense. google.gr/… . The complexity of real matter makes the continuum observed inevitable. –  anna v Jul 18 '13 at 19:35
So, an object with a very small number of particles would not be able to emit a continuous radiation curve like the blackbody curve? And this would be why you need atoms in a gasesous state to observe their spectra, so that the atoms are separated and each atom's energy levels are not affected by others. –  Joshua Jul 18 '13 at 21:13
@Joshua: Yes, that's correct. –  Ben Crowell Jul 18 '13 at 21:16

This is the second time in only a few days that I've cited Luboš Motl's excellent answer to What are the various physical mechanisms for energy transfer to the photon during blackbody emission?. As Luboš points out, the precise microscopic mechanisms of the radiation are unimportant because the statistical properties ensure that it follows Planck's law.

To get the characteristic black body curve you just need enough ways to generate EM radiation. Typically thermal vibrations in whatever material you're looking at result in accelerated electrons and oscillating dipoles within the material, and both generate the electromagnetic waves. This isn't a resonant process, so you don't get sharp lines but just a continuum of frequencies.

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