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Wien's displacement law

(Wien's law)
(temperature times wavelength with maximum intensity equals a constant)

Wien's displacement law states that within the black-body spectrum, the wavelength with the maximum intensity is inversely proportional to the temperature of the black body Graphs of the wavelength-distribution of emitted energy within black body radiation at various temperatures have the same general shape, but the peak is displaced within the graph, to a shorter wavelength of the temperature is higher, and vice versa:

wavelengthmax × temperature = b

In principle, this formula is used to determine the temperature of distant bodies such as stars. In practice, a rough determination would be done using a color index or brightness temperature, a more accurate determination would be done based upon the shape of the spectral energy distribution (SED) over some wavelength-range and an accurate temperature would take into account spectral features associated with temperatures and constituents both at and near the surface such as absorption lines.

Of note is that both the above constant and even the location of the peak are for graphs specifically mapping the wavelength to energy density per unit of wavelength of the EMR. An energy density per unit frequency peaks at a different wavelength, i.e., to a different wavelengthmax than the one described above. This latter peak is also inversely proportional to the black-body temperature, but the constant of proportionality used in this case must accommodate the measure the density is based on frequency. Energy density distributions can also be taken according to other units, such as log wavelength, or wavelength squared, and other means of characterizing the distribution have been used, such as the median of the energy distribution or the average photon energy and each of these has a constant of proportionality for its variant of Wien's displacement law. A particular type of instrument's sensitivity and resolution are oriented to just one of these (wavelength versus frequency, etc.). Alternate constants (using the above formula with temperature and wavelength):

Some example peaks:

temperature distribution by wavelength distribution by frequency distribution by log band
0.0285 K 1 m
294 MHz
1.8 m
1.68 MHz
1.29 m
233 MHz
radio
2.725 K 1.06 mm
282 GHz
1.87 mm
160 GHz
1.34 mm
222 GHz
microwave
273.15 K 10 μm
28 THz
18 μm
16 THz
13 μm
22 THz
mid infrared
300 K 9.66 μm
31 THz
17 μm
17 THz
12.2 μm
24.5 THz
mid infrared
6000 K 483 nm
621 THz
850 nm
353 THz
612 nm
490 THz
visible light
100,000 K 29 nm
10.3 PHz
51 nm
5.8 PHz
37 nm
8.2 PHz
extreme ultraviolet
1,000,000 K 2.9 nm
103 PHz
5.1 nm
58 PHz
3.7 nm
82 PHz
X-ray

(physics,EMR,wavelength,temperature,black body)
Further reading:
http://en.wikipedia.org/wiki/Wien%27s_displacement_law
http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html#c2

Referenced by pages:
angular power spectrum
black-body radiation
infrared (IR)
stellar temperature determination

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