December 14, 1900

Planck's law

Planck presents a statistical derivation of his radiation law using finite energy elements

Planck told his audience to divide energy into equal pieces — and, if the quotient was not a whole number, simply to choose a nearby integer.

14 December 1900: justifying a formula that already worked

At a meeting of the German Physical Society in Berlin on 14 December 1900, Max Planck presented 'Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum.' The talk did not unveil his radiation formula — he had presented that eight weeks earlier, on 19 October.

What it supplied was a derivation. Planck judged the October formula an inspired interpolation rather than a result from first principles, and turned to Boltzmann-style probability and state-counting to justify it.

Energy in countable pieces

He treated the total energy assigned to resonators as a finite number of equal elements, each defined as ε=hν, where ν is a resonator's frequency, and counted the possible distributions — 'complexions' — of those elements among the resonators. His worked example distributed 100 energy elements among ten numbered resonators.

The derivation reproduced the October radiation formula and related entropy to the logarithm of the number of possible energy distributions.

A constant in print, a revolution unnoticed

The paper printed h as 6.55 × 10⁻²⁷ erg·seconds and k as 1.346 × 10⁻¹⁶ erg per degree, from which Planck estimated 6.175 × 10²³ molecules per gram-molecule. Historians still dispute how literally he took the energy elements in 1900: the calculation discretised energy distributed among resonators, and did not clearly assert the photon concept Einstein introduced later.

By the end of the meeting the successful formula had a statistical derivation and a universal constant h, though its conceptual importance was not immediately appreciated.

Sources

Researched 23 Aug 2026 5 sources 3 audit passes

How this was checked

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What the sources leave uncertain

The date and presentation are well documented, but historians dispute how literally Planck regarded the energy elements in 1900. His calculation discretized the energy distributed among resonators; it did not clearly assert Einstein’s later photon concept, and some historians argue that it did not yet impose permanently discrete energies on individual resonators.