The Wien Radiation Law

The Wien law gives the wavelength of the peak of the radiation distribution:

Thus, the Wien law explains the shift of the peak to shorter wavelengths as the temperature increases. Notice that the variation of the peak of intensity with temperature is much less rapid than that of the intensity itself. The intensity varies as the fourth power of the temperature, but the peak position varies only inversely with T. For example, if T is doubled, the peak wavelength is decreased by a factor of two but the peak height is increased by a factor of sixteen.

The Wien Law in Action
The following figure illustrates the Wien law in action for three different stars of quite different surface temperature. The strong shift of the spectrum to shorter wavelengths with increasing temperatures is apparent in this illustration.

For convenience in plotting, these distributions have been normalized to unity at the respective peaks; by the Stefan-Boltzmann law, the area under the peak for the hot star Spica is in reality 2094 times the area under the peak for the cool star Antares.

Characteristic Temperatures
All heated objects emit a characteristic spectrum of electromagnetic radiation, and by the Wien law this spectrum is concentrated in longer wavelengths for cooler bodies. The following table summarizes the blackbody temperatures necessary to give a peak for emitted radiation in various regions of the spectrum.

Some Blackbody Temperatures
Region Wavelength
(centimeters)		 Energy
(eV)		 Blackbody Temperature
(K)
Radio > 10 < 10-5 < 0.03
Microwave 10 - 0.01 10-5 - 0.01 0.03 - 30
Infrared 0.01 - 7 x 10-5 0.01 - 2 30 - 4100
Visible 7 x 10-5 - 4 x 10-5 2 - 3 4100 - 7300
Ultraviolet 4 x 10-5 - 10-7 3 - 103 7300 - 3 x 106
X-Rays 10-7 - 10-9 103 - 105 3 x 106 - 3 x 108
Gamma Rays < 10-9 > 105 > 3 x 108

(The notation "eV" stands for electron-Volt, a common unit of energy.) As noted in the right panel, the peak temperatures quoted in this table are valid only if the spectrum is a thermal (blackbody) spectrum. The behavior of a nonthermal spectrum is not governed by the Wien law.