Astrophysics (Index) | About |

**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:

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, 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 wavelength_{max}
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):

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

http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html#c2

angular power spectrum

black-body radiation

infrared (IR)

stellar temperature determination