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So in what Planck called "an act of desperation", [91] he turned to Boltzmann's atomic law of entropy as it was the only one that made his equation work. Therefore, he used the Boltzmann constant k and his new constant h to explain the blackbody radiation law which became widely known through his published paper.
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: =.
Through Planck's law the temperature spectrum of a black body is proportionally related to the frequency of light and one may substitute the temperature (T) for the frequency in this equation. For the case of a source moving directly towards or away from the observer, this reduces to T ′ = T c − v c + v . {\displaystyle T'=T{\sqrt {\frac {c ...
Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths). This expression included a constant, h {\displaystyle h} , which is thought to be for Hilfsgröße (auxiliary quantity), [ 8 ] and subsequently became known as the Planck constant.
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.
The de Broglie equations relate the wavelength λ to the modulus of the momentum | | =, and frequency f to the total energy E of a free particle as written above: [54] = | | = = = where h is the Planck constant. The equations can also be written as = =, Here, ħ = h/2π is the reduced Planck constant.
The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the Planck constant. Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of ...
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.