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σ λ is their absorption cross-section at wavelength λ (units: area) B λ (T) is the Planck function for temperature T and wavelength λ (units: power/area/solid angle/wavelength - e.g. watts/cm 2 /sr/cm) I λ is the spectral intensity of the radiation entering the increment ds with the same units as B λ (T)
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 spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum.It is usually denoted by , and is closely related to the resolving power of the spectrograph, defined as =, where is the smallest difference in wavelengths that can be distinguished at a wavelength of .
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write: =where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m 2 = kg·m −1 ·s −3); Φ is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m 2); and λ is the wavelength (SI unit: meter, m).
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 ...
This holds for any trial φ since, by definition, the ground state wavefunction has the lowest energy, and any trial wavefunction will have energy greater than or equal to it. Proof: φ can be expanded as a linear combination of the actual eigenfunctions of the Hamiltonian (which we assume to be normalized and orthogonal): ϕ = ∑ n c n ψ n ...
In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule. [1] [2] For example, if an emissive state has a small oscillator strength, nonradiative decay will outpace radiative decay.
In slightly different terms, the emissive power of an arbitrary opaque body of fixed size and shape at a definite temperature can be described by a dimensionless ratio, sometimes called the emissivity: the ratio of the emissive power of the body to the emissive power of a black body of the same size and shape at the same fixed temperature. With ...