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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.
Additionally, using equation f = c/λ, = where E is the photon's energy; λ is the photon's wavelength; c is the speed of light in vacuum; h is the Planck constant; The photon energy at 1 Hz is equal to 6.626 070 15 × 10 −34 J, which is equal to 4.135 667 697 × 10 −15 eV.
These quanta would have an energy given by the Planck–Einstein relation: = and a momentum vector | | = = =, where ν (lowercase Greek letter nu) and λ (lowercase Greek letter lambda) denote the frequency and wavelength of the light, c the speed of light, and h the Planck constant. [3]
It equals the spatial frequency. 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.
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]
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.
Absorption or emission of a particle of light or photon corresponds to a transition between two possible energy levels, and the photon energy equals the difference between their two energies. On dividing by hc, the photon wavenumber equals the difference between two terms, each equal to an energy divided by hc or an energy in wavenumber units ...