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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 Compton wavelength for this particle is the wavelength of a photon of the same energy. For photons of frequency f , energy is given by E = h f = h c λ = m c 2 , {\displaystyle E=hf={\frac {hc}{\lambda }}=mc^{2},} which yields the Compton wavelength formula if solved for λ .
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.
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.
These peaks are the mode energy of a photon, when binned using equal-size bins of frequency or wavelength, respectively. Dividing hc (14 387.770 μm·K) by these energy expression gives the wavelength of the peak. The spectral radiance at these peaks is given by:
To find the wavelength equivalent to a moving body, de Broglie [2]: 214 set the total energy from special relativity for that body equal to hν: = = (Modern physics no longer uses this form of the total energy; the energy–momentum relation has proven more useful.)
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.
The quantity h / m e c is known as the Compton wavelength of the electron; it is equal to 2.43 × 10 −12 m. The wavelength shift λ′ − λ is at least zero (for θ = 0°) and at most twice the Compton wavelength of the electron (for θ = 180°).