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A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to identify atoms and molecules.
Spectral line shape or spectral line profile describes the form of an electromagnetic spectrum in the vicinity of a spectral line – a region of stronger or weaker intensity in the spectrum. Ideal line shapes include Lorentzian , Gaussian and Voigt functions, whose parameters are the line position, maximum height and half-width. [ 1 ]
A pair of graphs are said to be cospectral mates if they have the same spectrum, but are non-isomorphic. The smallest pair of cospectral mates is {K 1,4, C 4 ∪ K 1}, comprising the 5-vertex star and the graph union of the 4-vertex cycle and the single-vertex graph, as reported by Collatz and Sinogowitz [1] [2] in 1957.
The spectral lines are grouped into series according to n′. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the 2 → 1 line is called "Lyman-alpha" (Ly-α), while the 7 → 3 line is called "Paschen-delta" (Pa-δ).
There is disagreement in the literature for some line designations; for example, the Fraunhofer d line may refer to the cyan iron line at 466.814 nm, or alternatively to the yellow helium line (also labeled D 3) at 587.5618 nm. Similarly, there is ambiguity regarding the e line, since it can refer to the spectral lines of both iron (Fe) and ...
The pseudo-Voigt function is often used for calculations of experimental spectral line shapes. The mathematical definition of the normalized pseudo-Voigt profile is given by V p ( x , f ) = η ⋅ L ( x , f ) + ( 1 − η ) ⋅ G ( x , f ) {\displaystyle V_{p}(x,f)=\eta \cdot L(x,f)+(1-\eta )\cdot G(x,f)} with 0 < η < 1 {\displaystyle 0<\eta <1} .
For low optical depth corresponding to low , increasing the thickness of the medium leads to a linear increase of absorption and the equivalent line width grows linearly . Once the central Gaussian part of the profile saturates, τ ≈ 1 {\displaystyle \tau \approx 1} and the Gaussian tails will lead to a less effective growth of W ∝ ln N ...
The spectrometer uses a prism or a grating to spread the light into a spectrum. This allows astronomers to detect many of the chemical elements by their characteristic spectral lines. These lines are named for the elements which cause them, such as the hydrogen alpha, beta, and gamma lines. A glowing object will show bright spectral lines.