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| [[Image:Visible spectrum of hydrogen.jpg|600 px|thumb|The visible [[Hydrogen spectral series|hydrogen emission spectrum lines]] in the Balmer series. H-alpha is the red line at the right. The two leftmost lines are considered to be [[ultraviolet]] as they have wavelengths less than 400 nm.]]
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| The '''Balmer series''' or '''Balmer lines''' in [[atomic physics]], is the designation of one of a set of six different named series describing the [[spectral line]] emissions of the [[hydrogen atom]].
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| The Balmer series is calculated using the '''Balmer formula''', an [[empirical]] equation discovered by [[Johann Balmer]] in 1885.
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| The visible [[spectrum]] of [[light]] from [[hydrogen]] displays four [[wavelength]]s, 410 [[metre#SI prefixed forms of metre|nm]], 434 nm, 486 nm, and 656 nm, that correspond to emissions of [[photon]]s by [[electron]]s in excited states transitioning to the quantum level described by the [[principal quantum number]] ''n'' equals 2.<ref>C.R. Nave (2006). HyperPhysics: [http://hyperphysics.phy-astr.gsu.edu/Hbase/hyde.html#c4 ''Hydrogen Spectrum'']. Georgia State University. Accessed March 1st, 2008.</ref> There are also a number of [[ultraviolet]] Balmer lines with wavelengths shorter than 400 nm.
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| == Overview ==
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| [[Image:Bohr-atom-PAR.svg|thumb|left|210px|In the simplified '''[[Bohr model|Rutherford Bohr model]]''' of the [[hydrogen atom]], the Balmer lines result from an electron jump between the second energy level closest to the nucleus, and those levels more distant. Shown here is a photon emission. The <math>\scriptstyle 3 \rightarrow 2</math> transition depicted here produces [[H-alpha]], the first line of the Balmer series. For hydrogen (<math>Z = 1</math>) this transition results in a photon of [[wavelength]] 656 nm (red).]]
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| The Balmer series is characterized by the [[electron]] transitioning from ''n'' ≥ 3 to ''n'' = 2, where ''n'' refers to the [[radial quantum number]] or [[principal quantum number]] of the electron. The transitions are named sequentially by Greek letter: ''n'' = 3 to ''n'' = 2 is called H-α, 4 to 2 is H-β, 5 to 2 is H-γ, and 6 to 2 is H-δ. As the first spectral lines associated with this series are located in the visible part of the [[electromagnetic spectrum]], these lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen.
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| {| class="wikitable"
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| ! Transition of <math>n</math>
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| |align="center"|3→2
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| |align="center"|4→2
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| |align="center"|5→2
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| |align="center"|6→2
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| |align="center"|7→2
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| |align="center"|8→2
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| |align="center"|9→2
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| |align="center"|<math>\infty</math>→2
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| |-
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| ! Name
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| |align="center"|H-α / Ba-α
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| |align="center"|H-β / Ba-β
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| |align="center"|H-γ / Ba-γ
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| |align="center"|H-δ / Ba-δ
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| |align="center"|H-ε / Ba-ε
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| |align="center"|H-ζ / Ba-ζ
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| |align="center"|H-η / Ba-η
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| |-
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| ! Wavelength (nm) <ref>{{cite book|title=Quantum Physics|author=Eisberg and Resnick|publisher=John Wiley and Sons|year=1985|pages=97}}</ref>
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| |align="center"|656.3
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| |align="center"|486.1
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| |align="center"|434.1
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| |align="center"|410.2
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| |align="center"|397.0
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| |align="center"|388.9
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| |align="center"|383.5
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| |align="center"|364.6
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| |-
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| ! Color
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| |align="center"|[[Red]]
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| |align="center"|[[Cyan]]
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| |align="center"|[[Blue]]
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| |align="center"|[[Violet (color)|Violet]]
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| |align="center"|([[Ultraviolet]])
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| |align="center"|(Ultraviolet)
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| |align="center"|(Ultraviolet)
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| |align="center"|(Ultraviolet)
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| |}
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| Although physicists were aware of atomic emissions before 1885, they lacked a tool to accurately predict where the spectral lines should appear. The Balmer equation predicts the four visible absorption/emission lines of hydrogen with high accuracy. Balmer's equation inspired the [[Rydberg equation]] as a generalization of it, and this in turn led physicists to find the [[Lyman series|Lyman]], [[Paschen series|Paschen]], and [[Brackett series]] which predicted other absorption/emission lines of hydrogen found outside the [[visible spectrum]].
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| The familiar red [[H-alpha]] spectral line of hydrogen gas, which is the transition from the shell ''n'' = 3 to the Balmer series shell ''n'' = 2, is one of the conspicuous colours of the universe. It contributes a bright red line to the spectra of [[emission nebula|emission]] or ionisation nebula, like the [[Orion Nebula]], which are often [[H II region]]s found in star forming regions. In true-colour pictures, these nebula have a distinctly pink colour from the combination of visible Balmer lines that hydrogen emits.
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| Later, it was discovered that when the spectral lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely spaced doublets. This splitting is called [[fine structure]]. It was also found that excited electrons could jump to the Balmer series ''n''=2 from orbitals where ''n'' was greater than 6, emitting shades of violet when doing so.
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| [[Image:Deuterium lamp 1.png|thumb|right|300px|Two of the Balmer lines (α and β) are clearly visible in this emission spectrum of a [[deuterium lamp]].]] | |
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| == Balmer's formula ==
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| Balmer noticed that a single number had a relation to every line in the hydrogen spectrum that was in the [[visible light]] region. That number was 364.50682 nm. When any integer higher than 2 was squared and then divided by itself squared minus 4, then that number multiplied by 364.50682 (see equation below) gave a wavelength of another line in the hydrogen spectrum. By this formula, he was able to show that certain measurements of lines made in his time by [[spectroscopy]] were slightly inaccurate and his formula predicted lines that were later found although had not yet been observed. His number also proved to be the limit of the series.
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| The Balmer equation could be used to find the [[wavelength]] of the absorption/emission lines and was originally presented as follows (save for a notation change to give Balmer's constant as ''B''): | |
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| :<math>\lambda\ = B\left(\frac{n^2}{n^2 - m^2}\right) = B\left(\frac{n^2}{n^2 - 2^2}\right)</math>
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| Where
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| :<math>\lambda</math> is the wavelength.
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| :''B'' is a constant with the value of 3.6450682×10<sup>-7</sup> m or 364.50682 nm.
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| :''m'' is equal to 2
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| :''n'' is an integer such that ''n'' > ''m''.
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| In 1888 the physicist [[Johannes Rydberg]] generalized the Balmer equation for all transitions of hydrogen. The equation commonly used to calculate the Balmer series is a specific example of the [[Rydberg formula]] and follows as a simple reciprocal mathematical rearrangement of the formula above (conventionally using a notation of '''m''' for '''n''' as the single integral constant needed):
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| :<math>\frac{1}{\lambda} = \frac{4}{B}\left(\frac{1}{2^2} - \frac{1}{n^2}\right) = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right) \quad \mathrm{for~} n=3,4,5,...</math>
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| where λ is the wavelength of the absorbed/emitted light and ''R''<sub>H</sub> is the [[Rydberg constant]] for hydrogen. The Rydberg constant is seen to be equal to <math>4/B</math> in Balmer's formula, and this value, for an infinitely heavy nucleus, is <math>4/(3.6450682*10^{-7}</math> meter<math>)</math> = 10,973,731.57 meter<sup>−1</sup>.<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>
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| == Role in astronomy ==
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| The Balmer series is particularly useful in [[astronomy]] because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the [[universe]], and therefore are commonly seen and relatively strong compared to lines from other elements.
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| The [[stellar classification|spectral classification]] of stars, which is primarily a determination of surface temperature, is based on the relative strength of spectral lines, and the Balmer series in particular are very important. Other characteristics of a star that can be determined by close analysis of its spectrum include [[surface gravity]] (related to physical size) and composition.
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| Because the Balmer lines are commonly seen in the spectra of various objects, they are often used to determine [[Radial velocity|radial velocities]] due to [[doppler shift]]ing of the Balmer lines. This has important uses all over astronomy, from detecting [[binary star]]s, [[exoplanet]]s, compact objects such as [[neutron star]]s and [[black hole]]s (by the motion of hydrogen in [[accretion disk]]s around them), identifying groups of objects with similar motions and presumably origins ([[moving group]]s, [[star cluster]]s, [[galaxy cluster]]s, and debris from collisions), determining distances (actually [[redshift]]s) of galaxies or [[quasar]]s, and identifying unfamiliar objects by analysis of their spectrum.
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| Balmer lines can appear as [[absorption line|absorption]] or [[emission line|emission]] lines in a spectrum, depending on the nature of the object observed. In [[star]]s, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000 [[kelvin]] ([[spectral type]] A). In the spectra of most spiral and irregular galaxies, [[active galaxy|AGNs]], [[H II region]]s and [[planetary nebula|planetary]] [[nebula]]e, the Balmer lines are emission lines.
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| In stellar spectra, the H-epsilon line (transition 7-2) is often mixed in with another absorption line caused by ionized [[calcium]] known by astronomers as "H" (the [[Fraunhofer lines|original designation]] given by [[Joseph von Fraunhofer|Fraunhofer]]). That is, H-epsilon's wavelength is quite close to CaH at 396.847 nm, and cannot be resolved in low resolution spectra. The H-zeta line (transition 8-2) is similarly mixed in with a neutral [[helium]] line seen in hot stars.
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| == See also ==
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| * [[Hydrogen spectral series]]
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| * [[Astronomical spectroscopy]]
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| * [[Stellar classification]]
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| * [[Bohr model]]
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| * [[Theoretical and experimental justification for the Schrödinger equation]]
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| * [[Rydberg formula]]
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| == Notes ==
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| {{reflist}}
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| {{Hydrogen spectral series-footer}}
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| [[Category:Emission spectroscopy]]
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| [[Category:Hydrogen physics]]
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| [[Category:History of physics]]
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