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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: =.
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.
Photon energy is directly proportional to frequency. [1] = where is energy (joules in the SI system) [2] is the Planck constant; is frequency [2] This equation is known as the Planck relation. Additionally, using equation f = c/λ, = where
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.
Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. [3] [4] The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). For a modulated wave, wavelength may refer to the carrier wavelength of the signal.
Formally, the wavelength version of Wien's displacement law states that the spectral radiance of black-body radiation per unit wavelength, peaks at the wavelength given by: = where T is the absolute temperature and b is a constant of proportionality called Wien's displacement constant, equal to 2.897 771 955... × 10 −3 m⋅K, [1] [2] or b ...
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)
For example, a wavenumber in inverse centimeters can be converted to a frequency expressed in the unit gigahertz by multiplying by 29.979 2458 cm/ns (the speed of light, in centimeters per nanosecond); [5] conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space.