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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: =.
Photon energy can be expressed using any energy unit. Among the units commonly used to denote photon energy are the electronvolt (eV) and the joule (as well as its multiples, such as the microjoule). As one joule equals 6.24 × 10 18 eV, the larger units may be more useful in denoting the energy of photons with higher frequency and higher ...
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 ...
An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, N A = 6.022 140 76 × 10 23 mol −1, [36] with the result of 216 kJ, about the food energy ...
In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins. [123]
Massless particles have zero rest mass. The Planck–Einstein relation for the energy for photons is given by the equation E = hf, where h is the Planck constant and f is the photon frequency. This frequency and thus the relativistic energy are frame-dependent.
A particle of mass m has a rest energy of E = mc 2. 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 = = =, which yields the Compton wavelength formula if solved for λ.
The photon having non-zero linear momentum, one could imagine that it has a non-vanishing rest mass m 0, which is its mass at zero speed. However, we will now show that this is not the case: m 0 = 0. Since the photon propagates with the speed of light, special relativity is called for. The relativistic expressions for energy and momentum ...