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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 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 ...
This assumption allowed Planck to derive a formula for the entire spectrum of the radiation emitted by a black body. Planck was unable to justify this assumption based on classical physics; he considered quantization as being purely a mathematical trick, rather than (as is now known) a fundamental change in the understanding of the world. [1]
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: =.
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.
The Stefan–Boltzmann law may be expressed as a formula for radiance as a function of temperature. Radiance is measured in watts per square metre per steradian (W⋅m −2 ⋅sr −1 ). The Stefan–Boltzmann law for the radiance of a black body is: [ 9 ] : 26 [ 10 ] L Ω ∘ = M ∘ π = σ π T 4 . {\displaystyle L_{\Omega }^{\circ }={\frac ...
Historically, Planck derived the black body radiation law and detailed balance according to a classical thermodynamic argument, with a single heuristic step, which was later interpreted as a quantization hypothesis. [14] [15] In Planck's set up, he started with a large Hohlraum at a fixed temperature . At thermal equilibrium, the Hohlraum is ...
In 1900 Max Planck empirically obtained an expression for black-body radiation expressed in terms of wavelength λ = c/ν (Planck's law): =, where h is the Planck constant, and k B is the Boltzmann constant. Planck's law does not suffer from an ultraviolet catastrophe and agrees well with the experimental data, but its full significance (which ...