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Question:
What did Planck mean by energy "quanta". Was he saying that when producing radiation all the frequencies generated are not in a "continuum". That energy frequencies increased (or decreased) by a specific but constant amount. So that if a graph was plotted of all the frequencies in a black body at a given temperature the curve would be a series of dots rather than a continuous line. And the gaps between the dots are "quanta"?

To illustrate what I am trying to get at. If a black box actually generated infinite energy frequencies, and I plotted all of them on a sheet of graph paper I would end up with a solid black sheet. But if frequencies are generated in "quanta" and I plotted them, I would end up with a series of black lines distinctly separated. Like "fingerprints".



Replies:
Some authors have chosen to call this "temperature radiation", which is perhaps less confusing, since in common usage, a "blackbody" means something different. As a preamble, it should be emphasized that at the time, there was no satisfactory explanation of temperature radiation. The computation of the wavelength distribution, or equivalently the frequency distribution, was self-evident to any knowledgeable physicist of the day, and it was iron clad, there was no waffling out of the consequences of the classical physics. This space is to limited to go through those derivations, but the were inescapable in their conclusions. The only problem was the conclusions did not agree with observation -- equally iron clad. The classical derivation in fact predicted that there should be more and more radiation at shorter wavelengths -- the so-called "ultraviolet catastrophe". With a great leap of intuitive insight Planck asked himself what has to be done to make the theory come into agreement with the observed distribution of temperature radiation. His insight was to make the ad hoc assumption (at the time) that the possible energies of a mode of vibration of frequency 'f' in a radiation field were: 0, e, 2e,3e,..., where e = h x f (the constant of proportionality being subsequently named appropriately, Planck's constant). Then according to Boltzman's theory, the probability of each mode of vibration would be 1: exp(-e/kT): exp(-2e/kT): ...: exp(-ne/kT) This saved the radiation field from the "ultraviolet catastrophe" because exp(-ne/kT) meant that the probability decreased exponentially with increasing energy. After some fairly fundamental algebra he derived the frequency distribution that was actually observed. Now addressing your question directly, it is the very tiny value of the constant of proportionality, h = 6.6x10^-34 J*sec. This spacing is so small that on any reasonable graphing scale you cannot "see" the quantum "dots".

Vince Calder



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