Wien approximation

Wien's law of radiation was an empirical test of Wilhelm Wien to describe by a black body thermal radiation emitted as a function of wavelength. There is Wien's displacement law properly again.

History

Based on the experimental studies of Josef Stefan and the thermodynamic derivation by Ludwig Boltzmann was known that from a black body with the absolute temperature T thermally emitted radiation power increases with the fourth power of the temperature ( Main article: Stefan- Boltzmann law ). However, the distribution of the radiation energy to the various emitted wavelengths was still unknown.

Wien 's displacement law could be derived, which produced a correlation between the wave length distributions at various temperatures due to thermodynamic considerations:

" If you think of [ ... ] the energy plotted as a function of wavelength at a temperature, this curve would remain unchanged at different temperature when the standard of drawing would be changed so that the ordinates reduced in proportion 1/θ4 and the abscissae in the ratio would be increased θ. "

So that the wavelength distribution of the radiation was still unknown, but there was an additional condition found that the real wavelength distribution had to be subject to a temperature change. Today, this general form of the displacement law is no longer relevant because the Planck's radiation law, the spectral shift with temperature change concretely describes. Only the temperature-induced shift of the radiation maximum, which already follows from the displacement law, has survived under the name of vienna cal displacement law.

With the help of some additional assumptions Vienna could derive a radiation law, which on exposure to temperature changes behave as required by the law of displacement.

Definition

Wien's radiation law is in its by Wilhelm Wien in 1896 specified the form:

It has to be expected as a radiation maximum, but gives too low values ​​in the long wavelength range, see Fig.

Max Planck corrected this deficiency in 1900 by a clever interpolation between the Rayleigh-Jeans law (correct for large wavelengths ) and the Wien's radiation law (correct for small wavelengths). He found

And developed within a few weeks, the Planck's radiation law, which also applies as the birth of quantum physics. It is noteworthy that the constants adopted by Vienna C and c of Planck constants by nature Boltzmann's constant, the speed of light and the new constant h were expressed. The " auxiliary constant" h was later called Planck honor as Planck's constant.

Mean this

For small wavelengths λ or small temperatures T (in general, for small items λ · T) of the exponential term in the denominator of Planck's formula is large compared to unity. In these cases, the one to be compared with the larger term neglected and the Planckian formula goes over into the Wien's formula, which can be viewed in this sense as a limiting case of Planck's radiation law.