Planck's law gives the spectral distribution of electromagnetic energy emitted by a perfect thermal emitter (a black body) in equilibrium at absolute temperature T. It specifies how radiative power per unit area, per unit solid angle and per unit frequency or wavelength depends on temperature and frequency, and it established that energy exchange occurs in discrete quanta. The result resolved a long-standing contradiction between experiment and classical theory and became a foundation of modern physics.

Formulation and physical meaning

In common form the law gives the spectral radiance as a function of wavelength λ or frequency ν. Written in words, the radiance at a given wavelength is proportional to a prefactor involving fundamental constants and to 1 divided by the exponential of (energy quantum divided by thermal energy) minus one. The formula is usually presented with the Planck constant h, the speed of light c and the Boltzmann constant k; it implies the elementary energy associated with an oscillator of frequency ν is E = hν. That quantization is the key conceptual departure from classical continuous energy models.

History and development

The law was proposed in 1900 by Max Planck to reproduce measured blackbody spectra. Classical approaches, such as the Rayleigh–Jeans law, matched observation at long wavelengths but predicted an unphysical divergence at short wavelengths (the "ultraviolet catastrophe"). Planck's introduction of quantized energy elements produced the correct spectral shape and opened the path to the broader framework of quantum theory.

Planck's expression reduces to simpler approximations in limiting regimes: at low frequencies it approaches the Rayleigh–Jeans result, and at high frequencies it approaches Wien's approximation. Integrating Planck's law over all wavelengths yields the Stefan–Boltzmann law, which states that total emitted power per unit area scales as T^4, and differentiating it gives Wien's displacement relation for the peak wavelength, which moves to shorter wavelengths as temperature increases.

Uses, measurements and distinctions

Planck's law is central to fields that rely on thermal emission: astronomy (stellar and cosmic background spectra), remote sensing and climate science (Earth's thermal emission), radiometry and optical calibration, and infrared technology such as thermal imaging. Practical use requires choosing the spectral form (per unit wavelength or per unit frequency) because the numerical location of the spectral peak depends on that choice. Experimental fits to blackbody spectra provide temperature measurements and calibrate detectors that measure spectral density of electromagnetic radiation.

  • Key concept: energy quantization E = hν underlies the law.
  • Constants: involves h (Planck constant), c (speed of light) and k (Boltzmann constant).
  • Practical note: spectral radiance per unit wavelength and per unit frequency are not numerically identical and peak at different points.
  • Legacy: stimulated the development of modern physics and experimental techniques in spectroscopy.