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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.
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)
Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) ... is the Planck constant and ...
Planck's postulate was further applied to understanding the Compton effect, and was applied by Niels Bohr to explain the emission spectrum of the hydrogen atom and derive the correct value of the Rydberg constant.
where λ is the wavelength of an emitted photon, ν is its frequency, E is the photon energy, h is the Planck constant, and c is the speed of light in a vacuum. In a laboratory setting, the hydrogen line parameters have been more precisely measured as: λ = 21.106 114 054 160 (30) cm ν = 1 420 405 751.768(2) Hz. in a vacuum. [3]
From Planck's law of black-body radiation at temperature T we have for the spectral radiance (radiance is energy per unit time per unit solid angle per unit projected area, when integrated over an appropriate spectral interval) [26] at frequency ν (,) = /, where [27] =, where is the speed of light and is the Planck constant.
According to Planck's distribution law, the spectral energy density (energy per unit volume per unit frequency) at given temperature is given by: [4] [5] (,) = alternatively, the law can be expressed for the spectral radiance of a body for frequency ν at absolute temperature T given as: [6] [7] [8] (,) = where k B is the Boltzmann ...
In Dirac's theory the fields are quantized for the first time and it is also the first time that the Planck constant enters the expressions. In his original work, Dirac took the phases of the different electromagnetic modes ( Fourier components of the field) and the mode energies as dynamic variables to quantize (i.e., he reinterpreted them as ...