### 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
```
• wavelengthmax - 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 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):

• 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 m294 MHz 1.8 m1.68 MHz 1.29 m233 MHz radio 2.725 K 1.06 mm282 GHz 1.87 mm160 GHz 1.34 mm222 GHz microwave 273.15 K 10 μm28 THz 18 μm16 THz 13 μm22 THz mid infrared 300 K 9.66 μm31 THz 17 μm17 THz 12.2 μm24.5 THz mid infrared 6000 K 483 nm621 THz 850 nm353 THz 612 nm490 THz visible light 100,000 K 29 nm10.3 PHz 51 nm5.8 PHz 37 nm8.2 PHz extreme ultraviolet 1,000,000 K 2.9 nm103 PHz 5.1 nm58 PHz 3.7 nm82 PHz X-ray

(physics,EMR,wavelength,temperature,black body)