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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 in a black-body radiation, the wavelength with the maximum intensity is inversely proportional to the temperature of the black body. The wavelength distribution of black body radiation at any temperature has the same "shape" except that each wavelength is displaced on the graph.

wavelengthmax * Temperature = b

In principle, this formula is used to determine the temperature of distant bodies such as stars. In practice, typically more of the spectral energy distribution is evaluated to confirm the determined temperature, and complications such as EMR from different portions (e.g., layers) at different temperatures require accommodation.

Of note is that both the above constant and even the location of the peak depend upon the energy density per unit of wavelength of the EMR. An energy density per unit frequency produces a different EMR peak, i.e., a frequencymax that does not directly correspond to the wavelengthmax above. This latter peak is also directly proportional to the black-body temperature, but the constant of proportionality used in this case must not only accommodate the Planck constant, but this different type of peak. The energy density distribution 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, any of which has a constant of proportionality for a version of Wien's displacement law. A particular type of instrument's sensitivity and resolution may be oriented to 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
2.725 K 1.06 mm
282 GHz
1.87 mm
160 GHz
1.34 mm
222 GHz
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

(physics,EMR,wavelength,temperature,black body)
Further reading:

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