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Blackbody radiation - quantum to classical

  1. Jun 11, 2013 #1
    I have a question regarding the parameters that reduces the Planck distribution to the Rayleigh-Jeans distribution.

    According to the Planck distribution, the average energy in a unit volume in the [itex]\nu[/itex] frequency mode of a blackbody radiation field is [itex]<U> = \frac{h\nu}{e \frac{h\nu}{KT} - 1}[/itex]. And , I see that in both the limits [itex]\nu \rightarrow 0[/itex] and [itex]T \rightarrow \infty[/itex], the expression reduces to the classical Rayleigh-Jeans form.

    Are these two limits a part of the correspondence principle?
  2. jcsd
  3. Jun 12, 2013 #2

    Jano L.

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    Gold Member

    What do you mean by correspondence principle exactly?

    Mathematically, the above formula approaches ##kT## in both limits.

    In practice, we check the limit by keeping temperature close to common temperatures and look at low frequencies.

    The limit ##T\rightarrow\infty## is hard to realize.

    I think the comparison to ##kT## makes little sense as a check on the correctness of the Planck formula in this limit. Even in classical theory, the average energy should be lower than ##kT## for high temperatures.

    This is because the assumptions of Rayleigh and Jeans are very implausible for high temperatures; radiation has to be enclosed in a box with perfectly reflecting walls, but this is very unlikely to be possible, as the known metals melt down for temperatures higher than few thousand K. The Rayleigh-Jeans derivation has restricted validity even from the viewpoint of classical theory, although this is often being forgotten today.
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