- Wien approximation
Wien's approximation (also sometimes called "
Wien's law" or the "Wien distribution law") is a law of physicsused to describe the spectrumof thermal radiation (frequently called the blackbodyfunction). This law was first derived by Wilhelm Wienin 1896.cite book
author=J. Mehra, H. Rechenberg
title=The Historical Development of Quantum Theory
id=ISBN 0-387-90642-8] cite book
author=R. Bowley, M. Sánchez
title=Introductory Statistical Mechanics
id=ISBN 0-19-850576-0] The equation does accurately describe the short
wavelength(high frequency) spectrum of thermal emission from objects, but it fails to accurately fit the experimental data for long wavelengths(low frequency) emission.
The law may be written as
author=G. B. Rybicki, A. P. Lightman
title=Radiative Processes in Astrophysics
publisher=John Wiley & Sons
:* is the amount of
energyper unit surface areaper unit timeper unit solid angleper unit frequencyemitted at a frequency ν.:* is the temperatureof the black body.:* is Planck's constant.:* is the speed of light.:* is Boltzmann's constant.
This equation may also be written as
Equation derived using u=4π/c; see Rybicki, Lightman (1979) reference.]
where is the amount of
energyper unit surface areaper unit timeper unit solid angleper unit wavelengthemitted at a wavelength λ.
Relation to Planck's law
The Wien approximation was originally proposed as a description of the complete spectrum of thermal radiation, although it failed to accurately describe long wavelength (low frequency) emission. However, it was soon superseded by
Planck's law, developed by Max Planck. Unlike the Wien approximation, Planck's law accurately describes the complete spectrum of thermal radiation. Planck's law may be given as
The Wien approximation may be derived from Planck's law by assuming . When this is true, then
and so Planck's law approximately equals the Wien approximation at high frequencies.
Other approximations of thermal radiation
Rayleigh-Jeans lawdeveloped by Lord Rayleighmay be used to accurately describe the long wavelength spectrum of thermal radiation but fails to describe the short wavelength spectrum of thermal emission.
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