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Planck, Quanta, and Continuum
Name: William
Status: other
Age: N/A
Location: N/A
Country: N/A
Date: N/A
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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Update: June 2012
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