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The Planck constant, or Planck's constant, denoted by , [1] is a fundamental physical constant [1] of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.
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: =.
A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h /2 π , also known as the reduced Planck constant or Dirac constant . Quantity (common name/s)
Planck units modified so that 8 π G = 1 are known as reduced Planck units, because the Planck mass is divided by √ 8 π. Also, the Bekenstein–Hawking formula for the entropy of a black hole simplifies to S BH = (m BH) 2 /2 = 2 π A BH.
In 1905, "Einstein believed that Planck's theory could not be made to agree with the idea of light quanta, a mistake he corrected in 1906." [133] Contrary to Planck's beliefs of the time, Einstein proposed a model and formula whereby light was emitted, absorbed, and propagated in free space in energy quanta localized in points of space. [132]
since / = 1.239 841 984... × 10 −6 eV⋅m [4] where h is the Planck constant, c is the speed of light, and e is the elementary charge. The photon energy of near infrared radiation at 1 μm wavelength is approximately 1.2398 eV.
The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: =. Wave-like behavior of matter has been experimentally demonstrated, first for electrons in 1927 and for other elementary particles , neutral atoms and molecules in the years since.
[15] is a constant resulting from the maximization equation, k is the Boltzmann constant, h is the Planck constant, and T is the absolute temperature. With the emission now considered per unit frequency, this peak now corresponds to a wavelength about 76% longer than the peak considered per unit wavelength.