Astrophysics (Index)About

Planck function

(Planck's law)
(yields black-body spectrum curve)

The Planck function is a function of wavelength (or frequency) and temperature that describes a distribution of the intensity (aka radiance) at each wavelength or frequency (i.e., the specific intensity aka spectral radiance) in black-body radiation. The form for frequency:

         2hν3      1
B(ν,T) = ———— —————————————
          c2  ehν/(kBT) - 1

Note that the formula for the Plank function for the distribution over wavelength does not simply plug in c/wavelength into the above formula: the relation of their differentials must be taken into account.

Sometimes the equation is cited including π as an additional factor: the form with π produces the total energy emitted per unit area of the black body per wavelength or frequency, i.e., the spectral flux density a unit area produces.

Much of astrophysics uses the term intensity for the quantity of radiation emitted through a surface into a given solid angle, specific intensity being the radiance at a given wavelength or frequency. More common terms are radiance and spectral radiance.


(function,physics,EMR,black body)
Further reading:
https://en.wikipedia.org/wiki/Planck_function
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html#c3
http://spiff.rit.edu/classes/phys317/lectures/planck.html

Referenced by pages:
black-body radiation
brightness temperature (TB)
Kirchhoff's law of thermal radiation
noise-equivalent power (NEP)
Planck constant (h)
Rayleigh-Jeans law
Rosseland mean opacity
thermal emission
Wien approximation

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