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**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.

wavelength_{max}* Temperature = b

- wavelength
_{max}- wavelength with the greatest intensity. - Temperature - absolute temperature of the black body.
- b -
**Wien's displacement constant**: 2.8977685 × 10^{-3}m K

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 frequency_{max} that does *not* directly correspond to the
wavelength_{max} 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):

- For peak of distribution over frequency: 5.10 × 10
^{-3}K m - For peak of distribution over log of frequency or wavelength: 3.67 × 10
^{-3}K m

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 |

http://en.wikipedia.org/wiki/Wien%27s_displacement_law

angular power spectrum

black-body radiation

infrared (IR)

stellar temperature determination