Wien approximation

The high-frequency approximation to Planck’s radiation law, obtained by replacing the photon occupation factor’s denominator with its dominant exponential term. It yields an exponentially declining spectrum.

Planck’s law: The formula for the spectral distribution of electromagnetic radiation emitted by a body in thermal equilibrium. The Wien approximation emerges from Planck’s spectrum when photon energies greatly exceed thermal energy.
Wilhelm Wien: German physicist whose work on thermal radiation led to Wien’s displacement law and an early radiation spectrum formula. His radiation formula preceded Planck’s law and supplied the name for this limit.
Wien approximation in spectroscopy: Use of the high-frequency Planck spectrum to estimate thermal emission in a restricted spectral range. The exponential form can simplify calculations on the short-wavelength side of a thermal spectrum.
Rayleigh–Jeans approximation: The classical low-frequency limit of Planck’s radiation law. Its validity condition opposes the high-frequency condition required here.
Photon occupation number: The mean number of photons in a bosonic mode at thermal equilibrium. Its Bose–Einstein denominator is simplified to obtain the approximation.
Wien distribution law: An early formula proposed by Wilhelm Wien for the spectrum of blackbody radiation. The high-frequency form of Planck’s law recovers this earlier spectrum.
Planck spectral radiance: The power emitted by a blackbody per unit area, solid angle, and frequency or wavelength interval. The Wien approximation estimates this quantity in the high-frequency regime.
Planck radiation law exact form: The complete quantum expression for blackbody spectral radiation across all frequencies. Unlike the Wien approximation, it remains valid through the spectrum’s peak and both tails.
Bose–Einstein distribution: The equilibrium particle-number distribution for indistinguishable bosons. The photon occupation factor in Planck’s law has this distribution’s form.
Blackbody radiation: Electromagnetic radiation emitted by an ideal absorber in thermal equilibrium, with a spectrum determined by temperature. The approximation arose in attempts to describe this thermal spectrum.

Linked from 7 pages