Blackbody radiation and Planck's law

A blackbody is an idealised object that absorbs all radiation striking it and emits radiation determined purely by its own temperature — "black" describes its perfect absorption at every wavelength, not its literal colour, since a hot blackbody visibly glows. Its emission spectrum has a very specific shape: rising from long wavelengths, peaking somewhere, and falling off again at short wavelengths, with the whole curve shifting to shorter wavelengths as temperature increases — which is why a heated metal glows first dull red, then orange, then white as it gets hotter.

Late-nineteenth-century classical physics, treating the radiation as continuous electromagnetic waves able to carry any amount of energy, could predict the long-wavelength side of this curve correctly but failed catastrophically at short wavelengths: the theory predicted the emitted energy should keep rising without limit as wavelength shrank, implying every warm object should radiate infinite power in the ultraviolet and beyond — the ultraviolet catastrophe. This was not an observed result; it was a prediction manifestly contradicted by every actual measurement, which never showed anything like infinite emission.

Planck's resolution, in 1900, was to assume that the oscillators in the blackbody's walls could only emit or absorb energy in discrete packets, each of size hf, proportional to frequency, rather than in any continuous amount. At high frequencies (short wavelengths), each packet becomes so large that very few oscillators have enough energy to emit one at all, which suppresses short-wavelength emission and reproduces the observed spectrum exactly. Planck treated this quantisation as a mathematical device to fix the formula, without initially believing light itself was made of particles — that further step was Einstein's, five years later, explaining the photoelectric effect. Planck's assumption nonetheless marks the moment quantum mechanics began: the first time physics required energy to come in discrete quanta rather than flowing continuously.