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In physics, Planck's law (also Planck radiation law [1]: 1305 ) describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
The problem was solved in 1901 by Max Planck in the formalism now known as Planck's law of blackbody radiation. [26] By making changes to Wien's radiation law (not to be confused with Wien's displacement law) consistent with thermodynamics and electromagnetism, he found a mathematical expression fitting the experimental data satisfactorily ...
For a black body, Planck's law gives: [8] [11] = where (the Intensity or Brightness) is the amount of energy emitted per unit surface area per unit time per unit solid angle and in the frequency range between and +; is the temperature of the black body; is the Planck constant; is frequency; is the speed of light; and is the Boltzmann constant.
Deriving the Stefan–Boltzmann Law using Planck's law. The law can be derived by considering a small flat black body surface radiating out into a half-sphere. This derivation uses spherical coordinates , with θ as the zenith angle and φ as the azimuthal angle; and the small flat blackbody surface lies on the xy-plane, where θ = π / 2 .
Note that in the above formula for Planck's Law, you might as well use c 1L = 2hc 2 (the first radiation constant for spectral radiance) instead of c 1 (the “regular” first radiation constant), in which case the formula would give the spectral radiance L(λ,T) of the black body instead of the spectral radiant exitance M(λ,T).
In particular, Planck assumed that electromagnetic radiation can be emitted or absorbed only in discrete packets, called quanta, of energy: = =, where: h is the Planck constant, ν is the frequency of light, c is the speed of light, λ is the wavelength of light.
It is given by Planck's law per unit wavelength as:, (,) = / This formula mathematically follows from calculation of spectral distribution of energy in quantized electromagnetic field which is in complete thermal equilibrium with the radiating object. Planck's law shows that radiative energy increases with temperature, and explains why the peak ...