Re: the quantum hypothesis and blackbody radiation
- From: "C. M. Heard" <heard@xxxxxxxxx>
- Date: Thu, 26 Jan 2006 06:25:32 +0000 (UTC)
"Alex" <akhaneles at yahoo.com> wrote:
>>From the quantum hypothesis itself you can derive rather Wien's
>formula. Planck was trying to explain experimental data and his
>radiation law but it was not a theoretical prediction. From
>discontinuity of energy you can arrive only at Planck's mean energy
>distribution. To get Planck's radiation law you would need additional
>presumptions which are quite foreign to the quantum hypothesis.
I believe that you have this backwards. According to Wehr and
Richards, the textbook used in my Modern Physics class some 35
years ago, Wien's law was essentially an empirical curve fit.
Explicitly it reads
dE/dlambda = c1 lambda^-5 / exp(c2 / (lambda * T))
where c1 and c2 are empirically determined constants, lambda is
wavelength, and T is absolute temperature. This provides a good
fit to experimental results at short wavelengths but a poor fit
at long wavelengths, where it should reduce to the classical
Rayleigh-Jeans law. Planck did notice that one could improve
the fit by putting a minus one into the denominator, and this
indeed was another empirical step.
However, Planck also showed that one could rigorously derive
his law from the quantum hypothesis (i.e., that a harmonic
oscillator has allowed energy values of n h_cross omega) _and_
the result from statistical mechanics that the ratio of the
probabalites of occupancys of two states A and B is
exp(-EA/kT) / exp(-EB/kT).
//cmh
.
- Follow-Ups:
- Prev by Date: Re: orbitals, flowers, quantum puzzlement;
- Next by Date: Re: Newton's inverse-square force law from Einstein's equation
- Previous by thread: Re: the quantum hypothesis and blackbody radiation
- Next by thread: Re: the quantum hypothesis and blackbody radiation
- Index(es):
Relevant Pages
|
|
