Upon examining the curve describing blackbody thermal radiation, I noticed that the curves approaches (but never reaches) zero when increasing wavelength, but on the other hand it actually does reach zero at high frequency so I was wondering why?

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    $\begingroup$ Good question. This confused many physicist for years and was at the birth of quantum mechanics. $\endgroup$ Apr 4 at 1:20
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    $\begingroup$ What makes you think it reaches zero? $\endgroup$
    – G. Smith
    Apr 4 at 4:14
  • $\begingroup$ Let's state the behaviour carefully. Plotted against frequency, intensity scales as $\nu^3/(e^{\beta h\nu}-1)$, reaching $0$ at $\nu=0$ but not at any finite $\nu>0$. Plotted against wavelength, intensity scales as $\lambda^{-5}/(e^{\beta hc/\lambda}-1)$, which is asymptotic to $\lambda^{-5}e^{-\beta hc/\lambda}$ ($\lambda^{-4}/(\beta hc)$) for small (large) $\lambda>0$, so the $\lambda\to0^+,\,\lambda\to\infty$ one-sided limits are both $0$. $\endgroup$
    – J.G.
    Apr 4 at 20:47
  • $\begingroup$ There is a contradiction in the body of your question. $\endgroup$
    – my2cts
    May 11 at 11:05

In the frequency domain, the power spectral density has the form $f^2$ as the frequency approaches zero and the form $f^3e^{-f}$ as the freuency approaches infinity. In neither case does it reach zero at any finite frequency. You can argue about at which end it approaches zero more rapidly. Plotted on a log frequency axis, the high-frequency end of the spectrum would appear to approach zero very abruptly because of the exponential.


Classical (non-quantum) electrodynamics posits that for a radiating (hot) body, the number of available oscillation modes grows without bound at higher and higher frequencies, and so the energy carried by those modes blows up too at high frequencies- a result called the ultraviolet catastrophe which was decidedly not exhibited by actual hot objects in the laboratory where instead, as you point out, the energy contained per slice of the frequency spectrum falls towards zero with increasing frequency.

Max Planck fixed the ultraviolet catastrophe by deriving from scratch an entirely new function for the overall shape of the entire blackbody spectrum which was based on the premise that the energy being exchanged between the walls of the blackbody cavity and the radiation inside it was not a continuous variable but was subdivided into quantized (but very tiny) chunks instead.

Planck's full derivation is long and nontrivial but it works by making it progressively less likely with increasing frequency that there will be quanta sufficiently energetic to populate the highest-energy portions of the spectrum, suppressing the ultraviolet catastrophe and yielding a calculated shape for the spectrum which follows the real spectrum nearly perfectly at both low and high frequencies.

Many consider his breakthrough to represent the birth of quantum mechanics. To be sure, his work laid down the rails upon which mighty trains would soon run.

  • $\begingroup$ I know about the ultraviolet catastrophe. What i don't understand is why a blackbody hypothetically emits waves of ALL wavelengths/frequencies, yet when you examine planck's curve there is clearly an interval in which there is no intensity, in other words no waves emitted with such frequencies.Planck tried to minimize the contribution of high frequency oscillators but as i understand it he actually disimissed them altogether. $\endgroup$
    – physcanvas
    Apr 4 at 22:55

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