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{{Unreferenced stub|auto=yes|date=December 2009}} | |||
In [[physics]], the '''Lyman-alpha line''', sometimes written as '''Ly-<math>\alpha</math> line''', is a [[spectral line]] of [[hydrogen]], or more generally of [[Hydrogen-like atom|one-electron ions]], in the [[Lyman series]], emitted when the [[electron]] falls from the <math>n = 2</math> orbital to the <math>n = 1</math> orbital, where ''n'' is the [[principal quantum number]]. In hydrogen, its [[wavelength]] of 1215.668 [[angstrom]]s (121.6 nm or 1.216 × 10<sup>−7 </sup>m), corresponding to a [[frequency]] of 2.47 × 10<sup>15</sup> hertz, places the Lyman-alpha line in the [[vacuum ultraviolet]] part of [[ultraviolet]] in the electromagnetic spectrum. Lyman-alpha astronomy must therefore ordinarily be carried out by satellite borne instruments. | |||
Because of [[fine structure]] perturbations, the Lyman-alpha line splits into a doublet. Specifically, because of the electron's [[spin-orbit interaction]], the stationary eigenstates of the [[Perturbation theory (quantum mechanics)|perturbed]] [[Hamiltonian (quantum mechanics)|Hamiltonian]] must be labeled by the ''total'' [[Angular_momentum#Angular_momentum_in_quantum_mechanics|angular momentum]] ''j'' of the electron ([[spin (physics)|spin]] plus [[Azimuthal quantum number|orbital]]), not just the [[Azimuthal quantum number|orbital angular momentum]] <math>l</math>. In the <math>n = 2</math> orbital, there are two possible states, <math>j = 1/2</math> and <math>j = 3/2</math>, resulting in a spectral doublet. The <math>j = 3/2</math> state is of higher energy (less negative) and so is energetically farther from the <math>n = 1</math> orbital to which it is transitioning. Thus, the <math>j = 3/2</math> state is associated with the more energetic (shorter wavelength) spectral line in the doublet. | |||
A K-alpha, or K<sub>α</sub>, line analogous to the Lyman-alpha line for hydrogen, occurs in the high-energy induced emission spectra of all chemical elements, since it results from the same electron transition as in hydrogen. | |||
The equation for prediction of the frequency of this line (usually in the X-ray range for heavier elements), uses the same base-frequency as Lyman-alpha, but multiplied by a (Z−1)<sup>2</sup> factor to account for differing atomic numbers (Z) between elements, and is expressed in [[Moseley's law]]. The Lyman-alpha line as included in the rest of the hydrogen Lyman spectral series, is most simply described by the {n,m} = {1,2...} solutions to the empirical [[Rydberg formula]] (the Lyman-alpha frequency is produced by multiplying the Rydberg frequency for the atomic mass of hydrogen, R<sub>M</sub> (see [[Rydberg constant]]), by a factor of 1/1 - 1/2<sup>2</sup> = 3/4). Empirically, the Rydberg equation is in turn modeled by the semi-classic [[Bohr model]] of the atom. | |||
==See also== | |||
*[[Lyman-alpha forest]] | |||
*[[Lyman-alpha emitter]] | |||
*[[Lyman-alpha blob]] | |||
*[[Moseley's law]] | |||
*[[Lyman series]] | |||
*[[Bohr model]] | |||
*[[Lyman-break galaxy]] | |||
{{DEFAULTSORT:Lyman-Alpha Line}} | |||
[[Category:Atomic physics]] | |||
[[Category:Astronomical spectroscopy]] | |||
{{Atomic-physics-stub}} | |||
Revision as of 05:16, 29 January 2014
Template:Unreferenced stub In physics, the Lyman-alpha line, sometimes written as Ly- line, is a spectral line of hydrogen, or more generally of one-electron ions, in the Lyman series, emitted when the electron falls from the orbital to the orbital, where n is the principal quantum number. In hydrogen, its wavelength of 1215.668 angstroms (121.6 nm or 1.216 × 10−7 m), corresponding to a frequency of 2.47 × 1015 hertz, places the Lyman-alpha line in the vacuum ultraviolet part of ultraviolet in the electromagnetic spectrum. Lyman-alpha astronomy must therefore ordinarily be carried out by satellite borne instruments.
Because of fine structure perturbations, the Lyman-alpha line splits into a doublet. Specifically, because of the electron's spin-orbit interaction, the stationary eigenstates of the perturbed Hamiltonian must be labeled by the total angular momentum j of the electron (spin plus orbital), not just the orbital angular momentum . In the orbital, there are two possible states, and , resulting in a spectral doublet. The state is of higher energy (less negative) and so is energetically farther from the orbital to which it is transitioning. Thus, the state is associated with the more energetic (shorter wavelength) spectral line in the doublet.
A K-alpha, or Kα, line analogous to the Lyman-alpha line for hydrogen, occurs in the high-energy induced emission spectra of all chemical elements, since it results from the same electron transition as in hydrogen.
The equation for prediction of the frequency of this line (usually in the X-ray range for heavier elements), uses the same base-frequency as Lyman-alpha, but multiplied by a (Z−1)2 factor to account for differing atomic numbers (Z) between elements, and is expressed in Moseley's law. The Lyman-alpha line as included in the rest of the hydrogen Lyman spectral series, is most simply described by the {n,m} = {1,2...} solutions to the empirical Rydberg formula (the Lyman-alpha frequency is produced by multiplying the Rydberg frequency for the atomic mass of hydrogen, RM (see Rydberg constant), by a factor of 1/1 - 1/22 = 3/4). Empirically, the Rydberg equation is in turn modeled by the semi-classic Bohr model of the atom.