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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.
This equation is known as the Planck relation. 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.
In 1890, Rydberg proposed on a formula describing the relation between the wavelengths in spectral lines of alkali metals. [2]: v1:376 He noticed that lines came in series and he found that he could simplify his calculations using the wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement.
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: =.
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
To calculate the density of states we rewrite equation as follows: = , where n is the norm of the vector n = (n 1, n 2, n 3). For every vector n with integer components larger than or equal to zero, there are two photon states.
Determining the redshift of an object in this way requires a frequency or wavelength range. In order to calculate the redshift, one has to know the wavelength of the emitted light in the rest frame of the source: in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source.
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 ...
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