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Formulas for the various peak wavelengths and mean photon energy were taken from the Wikipedia Wien's displacement law page. The median and quartiles were computed by numerically integrating Planck's law ; however, for any who wish to avoid this, information on percentiles is given in the Planck's law article.
Comparison of Wien’s curve and the Planck curve. Wien's approximation (also sometimes called Wien's law or the Wien distribution law) is a law of physics used to describe the spectrum of thermal radiation (frequently called the blackbody function). This law was first derived by Wilhelm Wien in 1896.
Formally, the wavelength version of Wien's displacement law states that the spectral radiance of black-body radiation per unit wavelength, peaks at the wavelength given by: = where T is the absolute temperature and b is a constant of proportionality called Wien's displacement constant, equal to 2.897 771 955... × 10 −3 m⋅K, [1] [2] or b ...
A consequence of Wien's displacement law is that the wavelength at which the intensity per unit wavelength of the radiation produced by a black body has a local maximum or peak, , is a function only of the temperature: =, where the constant b, known as Wien's displacement constant, is equal to + 2.897 771 955 × 10 −3 m K. [31]
In fact the "strong version" is the "Wien’s fifth power law: "According to this law, the maximum energy of emitted radiation Em is directly proportional to the fifth power of absolute temperature i.e. 𝐸 𝑚 ∝ 𝑇 5 or 𝐸 𝑚 = 𝐾 𝑇 5." I love this kind of text speaking about power but writing energy of emitted radiation.
Wien's law or Wien law may refer to: . Wien approximation, an equation used to describe the short-wavelength (high frequency) spectrum of thermal radiation; Wien's displacement law, an equation that describes the relationship between the temperature of an object and the peak wavelength or frequency of the emitted light
A more physically informative version of such a law views empirical temperature as a chart on a hotness manifold. [ 43 ] [ 58 ] [ 60 ] While the zeroth law permits the definitions of many different empirical scales of temperature, the second law of thermodynamics selects the definition of a single preferred, absolute temperature , unique up to ...
The spectral index departs from this value at shorter wavelengths, for which the Rayleigh–Jeans law becomes an increasingly inaccurate approximation, tending towards zero as intensity reaches a peak at a frequency given by Wien's displacement law.