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| [[File:Hydrogen spectrum.svg|frame|right|The spectral series of hydrogen, on a [[logarithm]]ic scale.]]
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| The [[emission spectrum]] of atomic [[hydrogen]] is divided into a number of '''spectral series''', with wavelengths given by the [[Rydberg formula]]. These observed spectral lines are due to [[electrons]] making a [[atomic electron transition|transition]] between two [[energy levels]] in the atom. The classification of the series by the Rydberg formula was important in the development of [[quantum mechanics]]. The spectral series are important in astronomy for detecting the presence of hydrogen and calculating [[red shift|red shifts]].
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| ==Physics==
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| A hydrogen atom consists of an electron orbiting its [[atomic nucleus|nucleus]]. The [[electromagnetic force]] between the electron and the nuclear [[proton]] leads to a set of [[quantum states]] for the electron, each with its own energy. These states were visualized by the [[Bohr model]] of the hydrogen atom as being distinct [[orbits]] around the nucleus. Each energy state, or orbit, is designated by an integer, {{mvar|n}} as shown in the figure.
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| [[File:Hydrogen transitions.svg|thumb|left|400px|Electron transitions and their resulting wavelengths for hydrogen. Energy levels are not to scale.]]
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| Spectral emission occurs when an electron transitions, or jumps, from a higher energy state to a lower energy state. To distinguish the two states, the lower energy state is commonly designated as {{mvar|n′}}, and the higher energy state is designated as {{mvar|n}}. The energy of an emitted [[photon]] corresponds to the energy difference between the two states. Because the energy of each state is fixed, the energy difference between them is fixed, and the transition will always produce a photon with the same energy.
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| The spectral lines are grouped into series according to {{mvar|n′}}. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the {{nowrap|2 → 1}} line is called "Lyman-alpha" (Ly-α), while the {{nowrap|7 → 3}} line is called "Paschen-delta" (Pa-δ).
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| There are emission lines from hydrogen that fall outside of these series, such as the [[Hydrogen line|21 cm line]]. These emission lines correspond to much rarer atomic events such as [[hyperfine structure|hyperfine]] transitions.<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html |title=The Hydrogen 21-cm Line |accessdate=2009-03-18 |work=[[Hyperphysics]] |publisher=[[Georgia State University]] |date=2004-10-30 }}</ref> The [[fine structure]] also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections.<ref>{{cite book |last=Liboff |first=Richard L. |author-link=Richard Liboff |title=Introductory Quantum Mechanics |publisher=Addison-Wesley |year=2002 |isbn=0-8053-8714-5}}</ref>
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| ==Rydberg formula==
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| {{Main|Rydberg formula}}
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| The energy differences between levels in the Bohr model, and hence the wavelengths of emitted/absorbed photons, is given by the Rydberg formula:<ref>{{citation |last=Bohr |first=Niels |author-link=Niels Bohr |chapter=Rydberg's discovery of the spectral laws |editor-last=Kalckar |editor-first=J. |title=N. Bohr: Collected Works |publisher=North-Holland Publ. |publication-place=Amsterdam |publication-date=1985 |volume=10 |pages=373–9}}</ref>
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| :<math> {1 \over \lambda} = R \left( {1 \over (n^\prime)^2} - {1 \over n^2} \right) \qquad \left( R = 1.097373 \times 10^7 \ \mathrm{m}^{-1} \right)</math>
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| where {{mvar|n}} is the upper energy level, {{mvar|n′}} is the lower energy level, and {{mvar|R}} is the [[Rydberg constant]].<ref name="CODATA">{{cite web |url=http://physics.nist.gov/cuu/Constants/codata.pdf |title=CODATA Recommended Values of the Fundamental Physical Constants: 2006 |work=Committee on Data for Science and Technology (CODATA) |publisher=[[NIST]]|format=PDF}}</ref> Meaningful values are returned only when {{mvar|n}} is greater than {{mvar|n′}} and the limit of one over infinity is taken to be zero. | |
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| ==Series==
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| All wavelengths are given to 3 [[significant figures]].
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| ===Lyman series (''n′'' = 1)===
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| {{main|Lyman series}}
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| {| class="wikitable" border="1" style="float:left"
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| |-
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| ! {{mvar|n}} !! λ (nm)
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| |-
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| |2 || 122
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| |-
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| |3 || 103
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| |-
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| |4 || 97.3
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| |-
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| |5 || 95.0
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| |-
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| |6 || 93.8
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| |-
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| |<math>\infty</math> || 91.2
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| |}
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| [[File:LymanSeries.svg|thumb|righ|400px|[[Lyman series]] of [[hydrogen atom]] spectral lines in the [[ultraviolet]]]]
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| The series is named after its discoverer, [[Theodore Lyman]], who discovered the spectral lines from 1906–1914. All the wavelengths in the Lyman series are in the [[ultraviolet]] band.<ref>{{citation |last=Lyman |first=Theodore |author-link=Theodore Lyman |title=The Spectrum of Hydrogen in the Region of Extremely Short Wave-Length |journal=Memoirs of the American Academy of Arts and Sciences |volume=13 |issue=3 |series=New Series |pages=125–146 |jstor=25058084 |issn=0096-6134 |year=1906}}</ref><ref>{{citation |last=Lyman |first=Theodore |author-link=Theodore Lyman |title=An Extension of the Spectrum in the Extreme Ultra-Violet |year=1914 |journal=Nature |volume=93 |pages=241 |doi=10.1038/093241a0|bibcode = 1914Natur..93..241L }}</ref>
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| {{-}}
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| ===Balmer series (''n′'' = 2)===
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| {{main|Balmer series}}
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| {| class="wikitable" border="1" style="float:left"
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| ! {{mvar|n}} !! λ (nm)
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| |3 || 656.3
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| |4 || 486.1
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| |5 || 434.0
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| |6 || 410.2
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| |7 || 397.0
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| |-
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| |<math>\infty</math> || 365
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| |-
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| |}
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| Named after [[Johann Balmer]], who discovered the '''Balmer formula''', an [[empirical]] equation to predict the Balmer series, in 1885. Balmer lines are historically referred to as "[[H-alpha]]", "H-beta", "H-gamma" and so on, where H is the element hydrogen.<ref>{{citation |last=Balmer |first=J. J. |author-link=Johann Jakob Balmer |title=Notiz uber die Spectrallinien des Wasserstoffs |journal=Annalen der Physik |volume=261 |issue=5 |pages=80–87 |year=1885 |url=http://www3.interscience.wiley.com/journal/112487600/abstract |doi=10.1002/andp.18852610506|bibcode = 1885AnP...261...80B }}</ref> Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the [[Fraunhofer lines|solar spectrum]]. H-alpha is an important line used in astronomy to detect the presence of hydrogen.
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| [[File:Emission spectrum-H.svg|757px|thumb|center|The four visible hydrogen emission spectrum lines in the Balmer series. H-alpha is the red line at the right.]]
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| {{-}}
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| ===Paschen series (Bohr series) (''n′'' = 3)===
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| {| class="wikitable" border="1" style="float:left"
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| ! {{mvar|n}} !! λ (nm)
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| |4 || 1875
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| |5 || 1282
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| |6 || 1094
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| |7 || 1005
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| |8 || 955
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| | 9 || 923
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| |-
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| | 10 || 902
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| | 11 || 887
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| |<math>\infty</math> || 820
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| |}
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| Named after the [[Austria|Austro]]-[[Germany|German]] physicist [[Friedrich Paschen]] who first observed them in 1908. The Paschen lines all lie in the [[infrared]] band.<ref>{{citation |last=Paschen |first=Friedrich |author-link=Friedrich Paschen |year=1908 |title=Zur Kenntnis ultraroter Linienspektra. I. (Normalwellenlängen bis 27000 Å.-E.) |journal=Annalen der Physik |volume=332 |issue=13 |pages=537–570 |url=http://www3.interscience.wiley.com/journal/112500956/abstract |doi=10.1002/andp.19083321303|bibcode = 1908AnP...332..537P }}</ref>
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| {{-}}
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| ===Brackett series (''n′'' = 4)===
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| {| class="wikitable" border="1" style="float:left"
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| |-
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| ! {{mvar|n}} !! λ (nm)
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| |5 || 4050
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| |6 || 2624
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| |7 || 2165
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| |8 || 1944
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| |9 || 1817
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| |-
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| |<math>\infty</math> || 1458
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| |}
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| Named after the American physicist [[Frederick Sumner Brackett]] who first observed the spectral lines in 1922.<ref>{{citation |last=Brackett |first=Frederick Sumner |author-link=Frederick Sumner Brackett |year=1922 |title=Visible and infra-red radiation of hydrogen |journal=Astrophysical Journal |volume=56 |pages=154 |doi=10.1086/142697|bibcode = 1922ApJ....56..154B }}</ref>
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| {{-}}
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| ===Pfund series (''n′'' = 5)===
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| {| class="wikitable" border="1" style="float:left"
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| ! {{mvar|n}} !! λ (nm)
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| |6 || 7460
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| |7 || 4650
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| |8 || 3740
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| |9 || 3300
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| |10 || 3040
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| |-
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| |<math>\infty</math> || 2280
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| |}
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| Experimentally discovered in 1924 by [[August Herman Pfund]].<ref>{{citation |last=Pfund |first=A. H. |author-link=August Herman Pfund |title=The emission of nitrogen and hydrogen in infrared |year=1924 |journal=J. Opt. Soc. Am. |volume=9 |issue=3 |pages=193–196 |doi=10.1364/JOSA.9.000193}}</ref>
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| {{-}}
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| ===Humphreys series (''n′'' = 6)===
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| {| class="wikitable" border="1" style="float:left"
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| ! {{mvar|n}} !! λ (nm)
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| |7 || 12400
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| |8 || 7500
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| |-
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| |9 || 5910
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| |10 || 5130
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| |11 || 4670
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| |<math>\infty</math> || 3280
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| |}
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| Discovered in 1953 by American physicist [[Curtis J. Humphreys]].<ref>{{citation |last=Humphreys |first=C.J. |author-link=Curtis J. Humphreys |title=Humphreys Series |journal=J. Research Natl. Bur. Standards |year=1953 |volume=50}}</ref>
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| {{-}}
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| ===Further (''n′'' > 6)===
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| Further series are unnamed, but follow exactly the same pattern as dictated by the Rydberg equation. Series are increasingly spread out and occur in increasing wavelengths. The lines are also increasingly faint, corresponding to increasingly rare atomic events.
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| == Extension to other systems ==
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| The concepts of the Rydberg formula can be applied to any system with a single particle orbiting a nucleus, for example a [[Helium|He]]<sup>+</sup> ion or a [[muonium]] exotic atom. The equation must be modified based on the system's [[Bohr radius]]; emissions will be of a similar character but at a different range of energies.
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| All other atoms possess at least two electrons in their [[ionization|neutral]] form and the interactions between these electrons makes analysis of the spectrum by such simple methods as described here impractical. The deduction of the Rydberg formula was a major step in physics, but it was long before an extension to the spectra of other elements could be accomplished.
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| ==See also==
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| * The [[hydrogen line]] (21 cm)
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| * [[Astronomical spectroscopy]]
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| * [[Moseley's law]]
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| * [[Theoretical and experimental justification for the Schrödinger equation]]
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| * [[Lyman series]]
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| * [[Balmer series]]
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| ==References==
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| {{reflist|colwidth=30em}}
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| == External links ==
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| *[http://www.bigs.de/BLH/en/index.php?option=com_content&view=category&layout=blog&id=50&Itemid=221 Spectral series of hydrogen animation]
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| [[Category:Hydrogen physics]]
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| [[Category:Emission spectroscopy]]
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| [[Category:Hydrogen]]
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Hello and welcome. My name is Irwin and I totally dig that name. South Dakota is exactly where me and my husband live and my family members enjoys it. Body building is one of the issues I adore most. Managing individuals is his profession.
My webpage :: www.buzzbit.net