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At equilibrium, the radiation inside this enclosure is described by Planck's law, as is the radiation leaving the small hole. Just as the Maxwell–Boltzmann distribution is the unique maximum entropy energy distribution for a gas of material particles at thermal equilibrium, so is Planck's distribution for a gas of photons .
Black-body radiation has a characteristic, continuous frequency spectrum that depends only on the body's temperature, [8] called the Planck spectrum or Planck's law. The spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, and at room temperature most of the emission is in the infrared ...
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 ...
Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation). [7] This mathematical expression is now known as Planck's law.
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 law, including the theoretical prediction of the Stefan–Boltzmann constant as a function of the speed of light, the Boltzmann constant and the Planck constant, is a direct consequence of Planck's law as formulated in 1900.
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.
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 ...