Re: How did Max Planck determine the value of his constant?

Irwin,

That's a great question! Usually when we discuss Planck's constant it's easy to start with the photoelectric effect, where photons with a certain minimum frequency (and thus energy) are needed to knock electrons free from the surface of a metal or semiconductor. But Einstein's famous article describing how this effect worked (using Planck's constant) wasn't published until 1905, four years after Planck introduced his constant h.

Planck was a theorist, not an experimentalist, so his work was based on analyzing published results by other physicists. Planck's 1901 paper was a new method to derive the spectrum of black body radiation based on new experimental results.

A black body at a certain temperature emits electromagnetic radiation with a certain spectrum, and physicists in the late 1800s were carefully studying this phenomenon (as well as spectroscopy; the "real" physics wasn't understood but the phenomena could be measured reasonably accurately with the equipment available at that time).

In 1900, new measurements of the black body spectrum showed significant deviations at longer wavelengths from earlier, classically derived formulae by Planck and Wilhelm Wien. Planck believed strongly in entropy as a fundamental process, and his paper attempted to explain this new data from the starting point of calculating the entropy of a large number of discrete classical resonators.

Interestingly he did not understand his work to imply that light was quantized; even years later he was a proponent of classical electrodynamics. Planck didn't even believe there was any physical significance to his assumption of discrete oscillators. He just thought of them as a convenient way make the math fit the data at all wavelengths. His constant h was just a fit (albeit a pretty accurate one) to the available data.

The actual derivation is a bit involved, but here is Planck's original 1901 paper (in translation).The original calculation of Planck's constant is at the very end of the paper. The link I gave above to the Wikipedia article on black body radiation also has a good discussion of Planck and the historical context of his work.