In my new found passion to understand the "inner meaning" of this thing called quantum theory, I've been trying to find Planck's derivation of -- or explanation for choosing -- the "constant of nature" that has become so popular.

I expected to be able to find the empirical basis for it very easily on google, but all I could find were explanations like, "a photon is a unit of radiation whose energy content can be found by E=hv." Well, this doesn't help me too much.

The closest thing I have been able to find to an "explanation" is from this article...

You can measure it experimentally.
You use a vacuum tube and excite electrons from the cathode with a light source of known wavelength and measure the voltage accross the tube.
You can then get h/e from the slope - without having to know the work function of the cathode. If you know e you can get h.

It fitted an equation to experimental data, in his case of dependence of intensity of radiation on frequency for black body, that was the start of it all.

Milikan did it originally in 1916 but you still have to pay for access to the paper ! http://focus.aps.org/story/v3/st23
There are lots of ugrad lab classes on the web describing it.

Thanks for the heads up on Milikan. However, the question still remains: What was Planck's justification for using it in 1900? I mean, how did the inventor of h derive it?

Sorry - Planck didn't measure it, and apparently didn't really believe in it!
He just realised mathemtically that if you made energy changes only available in discrete lumps it solved some problems in thermodynamics. Einstein used the idea to explain the photoelectric effect - so it's really as much Einstein's constant as Planck's.

Sometimes it takes centuries for the experiment to measure a constant proposed by a theory - it took a long time for the speed of light and the gravitational constant G to be measured accurately.

Planck came up with the idea of quantized radiation and the constant we know as h, in deriving a formula to fit the observed spectrum from a hot "black body." The details are covered in many introductory modern physics textbooks, e.g. Beiser, "Concepts of Modern Physics", section 2.2; Krane, "Modern Physics", section 3.3; Ohanian, "Modern Physics", section 3.1.

You might find these details on line by Googling for "black body radiation" or "blackbody radiation" or "Planck radiation formula".

So, where in the heck did it come from? Did manna from heaven fall into his lap?

Why did he pick these precise discrete lumps that now seem to fit so perfectly with empirical observation? Are you saying that the mathematics just "manifested it"?

I don't think that a constant is the reason why the Rayleigh-Jeans Law was a failure. Wein's displacement law is the thing that corrected it, and it had nothing to do with a simple constant.

No he came up with the idea that if you only allow energy to transfer in small lumps then some problems in thermodynamics are solved. He didn't need to know what value h had - just that it was very small.
It's the same as Newton's law of gravity - he knew that if the gravitational force was proportional the product of the masses and the distance squared then the orbits of planets worked out. It wasn't until a 100years later that Cavendish worked out what the value of 'G' was.

Interesting - I hadn't realisied Planck had actually got a value
You can derive it quite easily from Wien's law, which tells you frequency of the peak on the curve predicted by Planck's equation - of course this relies on you having a good value for Wien's constant!

Yes... this is all very interesting, indeed. I'm doing my best to trace this thing back in history. My guess that Boltzmann is going to end up being known as the "real" father of QM!

I'm sitting here reading Kuhn's "Black Body Theory and the Quantum Discontinuity 1894-1912". This is an extremely in depth look into the origins of QM.

The first mention of the "b" constant that eventually becomes Planck's "h" is mentioned here:

The internal quote from Planck is footnoted as: "Funfte Mittheilung" (Planck, 1899), p. 465; I, 585.