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Planck proposed that electromagnetic energy is emitted and absorbed in discrete quanta, each of energy E = hf, where h is Planck's constant and f is frequency. This hypothesis resolved the ultraviolet catastrophe by eliminating the classical prediction of infinite energy density in blackbody radiation. Quantization fundamentally changed our understanding of light-matter interaction.
You already know from blackbody radiation that a perfect absorber in thermal equilibrium emits a characteristic spectrum of electromagnetic radiation that depends only on temperature. You also know from classical wave theory that inside a cavity (representing the blackbody), there are countless possible standing-wave modes. The classical approach — the Rayleigh-Jeans law — assigns each mode an average energy of k_BT (from the equipartition theorem, since each mode is like a harmonic oscillator with two degrees of freedom). Counting the number of modes per unit frequency and multiplying by k_BT gives a spectral energy density that increases as f² — correctly matching experiment at low frequencies, but diverging to infinity at high frequencies. This is the ultraviolet catastrophe: classical physics predicts that a blackbody should radiate infinite power.
Planck's 1900 hypothesis cut off this divergence with a single bold assumption: the oscillators that emit and absorb radiation cannot take on arbitrary energies. Instead, they are quantized — an oscillator of frequency f can only have energies 0, hf, 2hf, 3hf, ... for some constant h. This changes the calculation dramatically. At high frequencies, a single quantum of energy hf becomes large compared to k_BT. Thermally exciting such a high-frequency mode requires a large energy fluctuation, which becomes exponentially improbable. The Boltzmann factor e−hf/k_BT suppresses the high-frequency modes, cutting off the divergence and giving the correct Planck distribution: the spectrum peaks at a frequency proportional to temperature (Wien's displacement law) and the total integrated power goes as T⁴ (Stefan-Boltzmann law) — both already known empirically and now derived from the hypothesis.
The mechanism of suppression is worth pausing on. In the classical picture, any mode can hold any amount of energy continuously, so on average each mode holds k_BT. In Planck's picture, a high-frequency mode is like a vending machine that only accepts large coins: most thermal energy parcels (of order k_BT) are too small to activate it. At low frequencies, hf ≪ k_BT, the quantum granularity is invisible, many quanta fit in each mode, and the classical equipartition result is recovered — which is why Rayleigh-Jeans works in the infrared. At high frequencies, hf ≫ k_BT, the quantization sharply limits the mode's occupation, and the spectrum falls off exponentially. The crossover happens at hf ≈ k_BT, which gives the peak frequency of the blackbody curve.
Planck himself was uncomfortable with the physical meaning of his hypothesis — he viewed it as a mathematical trick to get the right answer, not a literal statement about nature. It would take Einstein's 1905 analysis of the photoelectric effect to establish that light itself comes in discrete quanta (photons), not just the oscillators. But Planck's formula remains exact, and the constant h = 6.626 × 10⁻³⁴ J·s is now a foundational constant of nature, defining (along with c and k_B) the complete bridge between thermodynamics, electromagnetism, and quantum mechanics. Every quantum mechanical result carries Planck's constant implicitly, and the fact that h is small but not zero is precisely why macroscopic objects seem to follow classical physics while atoms do not.