How did Planck’s radiation law agree with blackbody-radiation experiments?

Max Planck’s radiation law successfully resolved the "ultraviolet catastrophe," a failure of classical physics where the Rayleigh-Jeans law predicted that energy emission would diverge to infinity at high frequencies.1

Unlike classical models that assumed energy was emitted as continuous waves, Planck theorized that energy is absorbed and radiated in discrete packets called quanta. He proposed that matter could only exchange energy at specific, equally spaced levels defined by the equation $E=nhf$, where $h$ is Planck’s constant and $f$ is the frequency.12

By incorporating this quantization, Planck’s radiation law provided a mathematical distribution that matched experimental observations across all frequencies, including the high-frequency ultraviolet range where previous theories failed. This groundbreaking work, which laid the foundation for quantum mechanics, aligned so precisely with empirical data that Planck was awarded the Nobel Prize for Physics in 1918.1