In 1894, Planck turned his attention to the problem of black-body radiation. The problem had been stated by Kirchhoff in 1859: "How does the intensity of the electromagnetic radiation emitted by a black body (a perfect absorber, also known as a cavity radiator) depend on the frequency of the radiation (i.e., the color of the light) and the temperature of the body?". The question had been explored experimentally, but no theoretical treatment had agreed with the experimentally observed evidence. Wilhelm Wien proposed Wien's law, which correctly predicted the behaviour at high frequencies, but failed at low frequencies. The Rayleigh–Jeans law, another approach to the problem, agreed with experimental results at low frequencies, but created what was later known as the "ultraviolet catastrophe" at high frequencies, as predicted by classical physics. However, contrary to many textbooks, this was not a motivation for Planck.

Planck's first proposed solution to the problem in 1899 followed from what he called the "principle of elementary disorder", which allowed him to derive Wien's law from a number of assumptions about the entropy of an ideal oscillator, creating what was referred to as the Wien–Planck law. Soon, however, it was found that experimental evidence did not confirm the new law at all, to Planck's frustration. He revised his approach and now derived the first version of the famous Planck black-body radiation law, which described clearly the experimentally observed black-body spectrum. It was first proposed in a meeting of the DPG on 19 October 1900 and published in 1901. (This first derivation did not include energy quantisation, and did not use statistical mechanics, to which he held an aversion.) In November 1900 Planck revised this first version, now relying on Boltzmann's statistical interpretation of the second law of thermodynamics as a way of gaining a more fundamental understanding of the principles behind his radiation law. Planck was deeply suspicious of the philosophical and physical implications of such an interpretation of Boltzmann's approach; thus his recourse to them was, as he later put it, "an act of despair ... I was ready to sacrifice any of my previous convictions about physics."

The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit:

E = h ? {\displaystyle E=h\nu }

where h is the Planck constant, also known as Planck's action quantum (introduced already in 1899), and ? is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by h? and not simply by ?. Physicists now call these quanta photons, and a photon of frequency ? will have its own specific and unique energy. The total energy at that frequency is then equal to h? multiplied by the number of photons at that frequency.

At first Planck considered that quantisation was only "a purely formal assumption ... actually I did not think much about it ..."; nowadays this assumption, incompatible with classical physics, is regarded as the birth of quantum physics and the greatest intellectual accomplishment of Planck's career. (Boltzmann had been discussing in a theoretical paper in 1877 the possibility that the energy states of a physical system could be discrete). The discovery of the Planck constant enabled him to define a new universal set of physical units (such as the Planck length and the Planck mass), all based on fundamental physical constants, upon which much of quantum theory is based. In a discussion with his son in December 1918 Planck described his discovery as 'a discovery of the first rank, comparable perhaps only to the discoveries of Newton.' In recognition of Planck's fundamental contribution to a new branch of physics, he was awarded the Nobel Prize in Physics for 1918; (he received the award in 1919).

Subsequently, Planck tried to grasp the meaning of energy quanta, but to no avail. "My unavailing attempts to somehow reintegrate the action quantum into classical theory extended over several years and caused me much trouble." Even several years later, other physicists such as Rayleigh, Jeans, and Lorentz set the Planck constant to zero in order to align with classical physics, but Planck knew well that this constant had a precise nonzero value. "I am unable to understand Jeans' stubbornness – he is an example of a theoretician as should never be existing, the same as Hegel was for philosophy. So much the worse for the facts if they don't fit."

Max Born wrote about Planck: "He was, by nature, a conservative mind; he had nothing of the revolutionary and was thoroughly skeptical about speculations. Yet his belief in the compelling force of logical reasoning from facts was so strong that he did not flinch from announcing the most revolutionary idea which ever has shaken physics."

Quantum Mechanics

At the end of the 1920s, Niels Bohr, Werner Heisenberg, and Wolfgang Pauli had worked out the Copenhagen interpretation of quantum mechanics, but it was rejected by Planck, and by Schrödinger, Laue, and Einstein as well. Planck expected that wave mechanics would soon render quantum theory – his own child – unnecessary. This was not to be the case, however. Further work only served to underscore the enduring central importance of quantum theory, even against his and Einstein's philosophical revulsions. Here Planck experienced the truth of his own earlier observation from his struggle with the older views during his younger years: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."