Re: Derivation of Planck Function

[Wes Davis <wlrdavis@EARTHLINK.NET>]

    I am really intrigued.  Since we are at the end of the school
year, I assume that you've taught all the classical stuff.  Can you
tell us what success you've had this year?  Have you taught your
secondary class on this level consistently?  In what kind of school
do you teach?

    Wes Davis





> After having taught college level physics for the past five years, I =
> am now teaching physics at the secondary level.  My lesson plan for t=
> he "introduction to quantum mechanics" involves an illustration of Ma=
> x Planck's quantum mechanics explanation of cavity radiation.  I set =
> the stage by having the students use their graphing calculators to pl=
> ay with the function y=3Dx^3/((e^cx)-1) where c=3D0.95, 0.85, ., 0.45=
> .  By doing this, they establish for themselves that the family of cu=
> rves are bounded (i.e., no ultraviolet catastrophe). =20
>
> =20
>
> I then schematically derive the Planck Function by introducing the co=
> ncept of the number of energy modes of cavity radiation per unit freq=
> uency proportional to frequency cubed, and then the number of modes p=
> er unit volume per frequency range.  I next discuss Planck's rejectio=
> n of equal energy participation over all modes-which leads to the "ca=
> tastrophe"-and discuss how Planck worked on the assumption that the e=
> nergy existed only in integral multiples of some lowest "quantum" amo=
> unt that was proportional to the frequency. =20
>
> =20
>
> It is when one next gets to the concept of the spectral density per f=
> requency interval and the average number of photons per mode that I f=
> ind really difficult to explain to the students; i.e., the statistica=
> l mechanics of the problem.  Of course, one gets out of this the aver=
> age number of photons per mode being 1/(e^ (beta h nu)-1). =20