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Hydrogen spectral series

The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an atom. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts.

The spectral series of hydrogen, on a logarithmic scale.

Physics edit

 
Electron transitions and their resulting wavelengths for hydrogen. Energy levels are not to scale.

A hydrogen atom consists of an electron orbiting its 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 level, or electron shell, or orbit, is designated by an integer, n as shown in the figure. The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory.

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 n′, and the higher energy state is designated as 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.

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).

 
Energy level diagram of electrons in hydrogen atom

There are emission lines from hydrogen that fall outside of these series, such as the 21 cm line. These emission lines correspond to much rarer atomic events such as hyperfine transitions.[1] The fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections.[2]

In quantum mechanical theory, the discrete spectrum of atomic emission was based on the Schrödinger equation, which is mainly devoted to the study of energy spectra of hydrogenlike atoms, whereas the time-dependent equivalent Heisenberg equation is convenient when studying an atom driven by an external electromagnetic wave.[3]

In the processes of absorption or emission of photons by an atom, the conservation laws hold for the whole isolated system, such as an atom plus a photon. Therefore the motion of the electron in the process of photon absorption or emission is always accompanied by motion of the nucleus, and, because the mass of the nucleus is always finite, the energy spectra of hydrogen-like atoms must depend on the nuclear mass.[3]

Rydberg formula edit

The energy differences between levels in the Bohr model, and hence the wavelengths of emitted or absorbed photons, is given by the Rydberg formula:[4]

 

where

Z is the atomic number,
n′ (often written  ) is the principal quantum number of the lower energy level,
n (or  ) is the principal quantum number of the upper energy level, and
  is the Rydberg constant. (1.09677×107 m−1 for hydrogen and 1.09737×107 m−1 for heavy metals).[5][6]

The wavelength will always be positive because n′ is defined as the lower level and so is less than n. This equation is valid for all hydrogen-like species, i.e. atoms having only a single electron, and the particular case of hydrogen spectral lines is given by Z=1.

Series edit

Lyman series (n′ = 1) edit

 
Lyman series of hydrogen atom spectral lines in the ultraviolet

In the Bohr model, the Lyman series includes the lines emitted by transitions of the electron from an outer orbit of quantum number n > 1 to the 1st orbit of quantum number n' = 1.

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.[7][8]

n λ, vacuum

(nm)

2 121.57
3 102.57
4 97.254
5 94.974
6 93.780
91.175
Source:[9]

Balmer series (n′ = 2) edit

 
The four visible hydrogen emission spectrum lines in the Balmer series. H-alpha is the red line at the right.

The Balmer series includes the lines due to transitions from an outer orbit n > 2 to the orbit n' = 2.

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.[10] 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 solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen.

n λ, air

(nm)

3 656.3  
4 486.1  
5 434.0  
6 410.2  
7 397.0  
364.6
Source:[9]

Paschen series (Bohr series, n′ = 3) edit

Named after the German physicist Friedrich Paschen who first observed them in 1908. The Paschen lines all lie in the infrared band.[11] This series overlaps with the next (Brackett) series, i.e. the shortest line in the Brackett series has a wavelength that falls among the Paschen series. All subsequent series overlap.

n λ, air

(nm)

4 1875
5 1282
6 1094
7 1005
8 954.6
820.4
Source:[9]

Brackett series (n′ = 4) edit

Named after the American physicist Frederick Sumner Brackett who first observed the spectral lines in 1922.[12] The spectral lines of Brackett series lie in far infrared band.

n λ, air

(nm)

5 4051
6 2625
7 2166
8 1944
9 1817
1458
Source:[9]

Pfund series (n′ = 5) edit

Experimentally discovered in 1924 by August Herman Pfund.[13]

n λ, vacuum

(nm)

6 7460
7 4654
8 3741
9 3297
10 3039
2279
Source:[14]

Humphreys series (n′ = 6) edit

Discovered in 1953 by American physicist Curtis J. Humphreys.[15]

n λ, vacuum

(μm)

7 12.37
8 7.503
9 5.908
10 5.129
11 4.673
3.282
Source:[14]

Further series (n′ > 6) edit

Further series are unnamed, but follow the same pattern and equation as dictated by the Rydberg equation. Series are increasingly spread out and occur at increasing wavelengths. The lines are also increasingly faint, corresponding to increasingly rare atomic events. The seventh series of atomic hydrogen was first demonstrated experimentally at infrared wavelengths in 1972 by Peter Hansen and John Strong at the University of Massachusetts Amherst.[16]

Extension to other systems edit

The concepts of the Rydberg formula can be applied to any system with a single particle orbiting a nucleus, for example a He+ 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. The Pickering–Fowler series was originally attributed to an unknown form of hydrogen with half-integer transition levels by both Pickering[17][18][19] and Fowler,[20] but Bohr correctly recognised them as spectral lines arising from the He+ nucleus.[21][22][23]

All other atoms have at least two electrons in their 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.

See also edit

References edit

  1. ^ "The Hydrogen 21-cm Line". Hyperphysics. Georgia State University. 2005-10-30. Retrieved 2009-03-18.
  2. ^ Liboff, Richard L. (2002). Introductory Quantum Mechanics. Addison-Wesley. ISBN 978-0-8053-8714-8.
  3. ^ a b Andrew, A. V. (2006). "2. Schrödinger equation". Atomic spectroscopy. Introduction of theory to Hyperfine Structure. p. 274. ISBN 978-0-387-25573-6.
  4. ^ Bohr, Niels (1985), "Rydberg's discovery of the spectral laws", in Kalckar, J. (ed.), N. Bohr: Collected Works, vol. 10, Amsterdam: North-Holland Publ., pp. 373–9
  5. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006" (PDF). Reviews of Modern Physics. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. CiteSeerX 10.1.1.150.3858. doi:10.1103/RevModPhys.80.633.
  6. ^ "Hydrogen energies and spectrum". hyperphysics.phy-astr.gsu.edu. Retrieved 2020-06-26.
  7. ^ Lyman, Theodore (1906), "The Spectrum of Hydrogen in the Region of Extremely Short Wave-Length", Memoirs of the American Academy of Arts and Sciences, New Series, 23 (3): 125–146, Bibcode:1906MAAAS..13..125L, doi:10.2307/25058084, JSTOR 25058084. Also in The Astrophysical Journal, 23: 181, 1906, Bibcode:1906ApJ....23..181L, doi:10.1086/141330{{citation}}: CS1 maint: untitled periodical (link).
  8. ^ Lyman, Theodore (1914), "An Extension of the Spectrum in the Extreme Ultra-Violet", Nature, 93 (2323): 241, Bibcode:1914Natur..93..241L, doi:10.1038/093241a0
  9. ^ a b c d Wiese, W. L.; Fuhr, J. R. (2009), "Accurate Atomic Transition Probabilities for Hydrogen, Helium, and Lithium", Journal of Physical and Chemical Reference Data, 38 (3): 565, Bibcode:2009JPCRD..38..565W, doi:10.1063/1.3077727
  10. ^ Balmer, J. J. (1885), "Notiz uber die Spectrallinien des Wasserstoffs", Annalen der Physik, 261 (5): 80–87, Bibcode:1885AnP...261...80B, doi:10.1002/andp.18852610506
  11. ^ Paschen, Friedrich (1908), "Zur Kenntnis ultraroter Linienspektra. I. (Normalwellenlängen bis 27000 Å.-E.)", Annalen der Physik, 332 (13): 537–570, Bibcode:1908AnP...332..537P, doi:10.1002/andp.19083321303, archived from the original on 2012-12-17
  12. ^ Brackett, Frederick Sumner (1922), "Visible and Infra-Red Radiation of Hydrogen", Astrophysical Journal, 56: 154, Bibcode:1922ApJ....56..154B, doi:10.1086/142697, hdl:2027/uc1.$b315747, S2CID 122252244
  13. ^ Pfund, A. H. (1924), "The emission of nitrogen and hydrogen in infrared", J. Opt. Soc. Am., 9 (3): 193–196, Bibcode:1924JOSA....9..193P, doi:10.1364/JOSA.9.000193
  14. ^ a b Kramida, A. E.; et al. (November 2010). "A critical compilation of experimental data on spectral lines and energy levels of hydrogen, deuterium, and tritium". Atomic Data and Nuclear Data Tables. 96 (6): 586–644. Bibcode:2010ADNDT..96..586K. doi:10.1016/j.adt.2010.05.001.
  15. ^ Humphreys, C.J. (1953), "The Sixth Series in the Spectrum of Atomic Hydrogen", Journal of Research of the National Bureau of Standards, 50: 1, doi:10.6028/jres.050.001
  16. ^ Hansen, Peter; Strong, John (1973). "Seventh Series of Atomic Hydrogen". Applied Optics. 12 (2): 429–430. Bibcode:1973ApOpt..12..429H. doi:10.1364/AO.12.000429. PMID 20125315.
  17. ^ Pickering, E. C. (1896). "Stars having peculiar spectra. New variable stars in Crux and Cygnus". Harvard College Observatory Circular. 12: 1–2. Bibcode:1896HarCi..12....1P. Also published as: Pickering, E. C.; Fleming, W. P. (1896). "Stars having peculiar spectra. New variable stars in Crux and Cygnus". Astrophysical Journal. 4: 369–370. Bibcode:1896ApJ.....4..369P. doi:10.1086/140291.
  18. ^ Pickering, E. C. (1897). "Stars having peculiar spectra. New variable Stars in Crux and Cygnus". Astronomische Nachrichten. 142 (6): 87–90. Bibcode:1896AN....142...87P. doi:10.1002/asna.18971420605.
  19. ^ Pickering, E. C. (1897). "The spectrum of zeta Puppis". Astrophysical Journal. 5: 92–94. Bibcode:1897ApJ.....5...92P. doi:10.1086/140312.
  20. ^ Fowler, A. (1912). "Observations of the Principal and other Series of Lines in the Spectrum of Hydrogen". Monthly Notices of the Royal Astronomical Society. 73 (2): 62–63. Bibcode:1912MNRAS..73...62F. doi:10.1093/mnras/73.2.62.
  21. ^ Bohr, N. (1913). "The Spectra of Helium and Hydrogen". Nature. 92 (2295): 231–232. Bibcode:1913Natur..92..231B. doi:10.1038/092231d0. S2CID 11988018.
  22. ^ Hoyer, Ulrich (1981). "Constitution of Atoms and Molecules". In Hoyer, Ulrich (ed.). Niels Bohr – Collected Works: Volume 2 – Work on Atomic Physics (1912–1917). Amsterdam: North Holland Publishing Company. pp. 103–316 (esp. pp. 116–122). ISBN 978-0720418002.
  23. ^ Robotti, Nadia (1983). "The Spectrum of ζ Puppis and the Historical Evolution of Empirical Data". Historical Studies in the Physical Sciences. 14 (1): 123–145. doi:10.2307/27757527. JSTOR 27757527.

External links edit

  Media related to Hydrogen spectral series at Wikimedia Commons

hydrogen, spectral, series, emission, spectrum, atomic, hydrogen, been, divided, into, number, spectral, series, with, wavelengths, given, rydberg, formula, these, observed, spectral, lines, electron, making, transitions, between, energy, levels, atom, classif. The emission spectrum of atomic hydrogen has been divided into a number of spectral series with wavelengths given by the Rydberg formula These observed spectral lines are due to the electron making transitions between two energy levels in an atom The classification of the series by the Rydberg formula was important in the development of quantum mechanics The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts The spectral series of hydrogen on a logarithmic scale Contents 1 Physics 2 Rydberg formula 3 Series 3 1 Lyman series n 1 3 2 Balmer series n 2 3 3 Paschen series Bohr series n 3 3 4 Brackett series n 4 3 5 Pfund series n 5 3 6 Humphreys series n 6 3 7 Further series n gt 6 4 Extension to other systems 5 See also 6 References 7 External linksPhysics editFurther information Hydrogen atom nbsp Electron transitions and their resulting wavelengths for hydrogen Energy levels are not to scale A hydrogen atom consists of an electron orbiting its 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 level or electron shell or orbit is designated by an integer n as shown in the figure The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory 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 n and the higher energy state is designated as 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 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 a while the 7 3 line is called Paschen delta Pa d nbsp Energy level diagram of electrons in hydrogen atomThere are emission lines from hydrogen that fall outside of these series such as the 21 cm line These emission lines correspond to much rarer atomic events such as hyperfine transitions 1 The fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines due to relativistic corrections 2 In quantum mechanical theory the discrete spectrum of atomic emission was based on the Schrodinger equation which is mainly devoted to the study of energy spectra of hydrogenlike atoms whereas the time dependent equivalent Heisenberg equation is convenient when studying an atom driven by an external electromagnetic wave 3 In the processes of absorption or emission of photons by an atom the conservation laws hold for the whole isolated system such as an atom plus a photon Therefore the motion of the electron in the process of photon absorption or emission is always accompanied by motion of the nucleus and because the mass of the nucleus is always finite the energy spectra of hydrogen like atoms must depend on the nuclear mass 3 Rydberg formula editMain article Rydberg formula The energy differences between levels in the Bohr model and hence the wavelengths of emitted or absorbed photons is given by the Rydberg formula 4 1 l Z 2 R 1 n 2 1 n 2 displaystyle 1 over lambda Z 2 R infty left 1 over n 2 1 over n 2 right nbsp where Z is the atomic number n often written n 1 displaystyle n 1 nbsp is the principal quantum number of the lower energy level n or n 2 displaystyle n 2 nbsp is the principal quantum number of the upper energy level and R displaystyle R infty nbsp is the Rydberg constant 1 09677 107 m 1 for hydrogen and 1 09737 107 m 1 for heavy metals 5 6 The wavelength will always be positive because n is defined as the lower level and so is less than n This equation is valid for all hydrogen like species i e atoms having only a single electron and the particular case of hydrogen spectral lines is given by Z 1 Series editLyman series n 1 edit nbsp Lyman series of hydrogen atom spectral lines in the ultravioletMain article Lyman series In the Bohr model the Lyman series includes the lines emitted by transitions of the electron from an outer orbit of quantum number n gt 1 to the 1st orbit of quantum number n 1 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 7 8 n l vacuum nm 2 121 573 102 574 97 2545 94 9746 93 780 91 175Source 9 Balmer series n 2 edit Main article Balmer series nbsp The four visible hydrogen emission spectrum lines in the Balmer series H alpha is the red line at the right The Balmer series includes the lines due to transitions from an outer orbit n gt 2 to the orbit n 2 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 10 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 solar spectrum H alpha is an important line used in astronomy to detect the presence of hydrogen n l air nm 3 656 3 nbsp 4 486 1 nbsp 5 434 0 nbsp 6 410 2 nbsp 7 397 0 nbsp 364 6Source 9 Paschen series Bohr series n 3 edit Named after the German physicist Friedrich Paschen who first observed them in 1908 The Paschen lines all lie in the infrared band 11 This series overlaps with the next Brackett series i e the shortest line in the Brackett series has a wavelength that falls among the Paschen series All subsequent series overlap n l air nm 4 18755 12826 10947 10058 954 6 820 4Source 9 Brackett series n 4 edit Named after the American physicist Frederick Sumner Brackett who first observed the spectral lines in 1922 12 The spectral lines of Brackett series lie in far infrared band n l air nm 5 40516 26257 21668 19449 1817 1458Source 9 Pfund series n 5 edit Experimentally discovered in 1924 by August Herman Pfund 13 n l vacuum nm 6 74607 46548 37419 329710 3039 2279Source 14 Humphreys series n 6 edit Discovered in 1953 by American physicist Curtis J Humphreys 15 n l vacuum mm 7 12 378 7 5039 5 90810 5 12911 4 673 3 282Source 14 Further series n gt 6 edit Further series are unnamed but follow the same pattern and equation as dictated by the Rydberg equation Series are increasingly spread out and occur at increasing wavelengths The lines are also increasingly faint corresponding to increasingly rare atomic events The seventh series of atomic hydrogen was first demonstrated experimentally at infrared wavelengths in 1972 by Peter Hansen and John Strong at the University of Massachusetts Amherst 16 Extension to other systems editThe concepts of the Rydberg formula can be applied to any system with a single particle orbiting a nucleus for example a He 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 The Pickering Fowler series was originally attributed to an unknown form of hydrogen with half integer transition levels by both Pickering 17 18 19 and Fowler 20 but Bohr correctly recognised them as spectral lines arising from the He nucleus 21 22 23 All other atoms have at least two electrons in their 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 See also editAstronomical spectroscopy The hydrogen line 21 cm Lamb shift Moseley s law Quantum optics Theoretical and experimental justification for the Schrodinger equationReferences edit The Hydrogen 21 cm Line Hyperphysics Georgia State University 2005 10 30 Retrieved 2009 03 18 Liboff Richard L 2002 Introductory Quantum Mechanics Addison Wesley ISBN 978 0 8053 8714 8 a b Andrew A V 2006 2 Schrodinger equation Atomic spectroscopy Introduction of theory to Hyperfine Structure p 274 ISBN 978 0 387 25573 6 Bohr Niels 1985 Rydberg s discovery of the spectral laws in Kalckar J ed N Bohr Collected Works vol 10 Amsterdam North Holland Publ pp 373 9 Mohr Peter J Taylor Barry N Newell David B 2008 CODATA Recommended Values of the Fundamental Physical Constants 2006 PDF Reviews of Modern Physics 80 2 633 730 arXiv 0801 0028 Bibcode 2008RvMP 80 633M CiteSeerX 10 1 1 150 3858 doi 10 1103 RevModPhys 80 633 Hydrogen energies and spectrum hyperphysics phy astr gsu edu Retrieved 2020 06 26 Lyman Theodore 1906 The Spectrum of Hydrogen in the Region of Extremely Short Wave Length Memoirs of the American Academy of Arts and Sciences New Series 23 3 125 146 Bibcode 1906MAAAS 13 125L doi 10 2307 25058084 JSTOR 25058084 Also in The Astrophysical Journal 23 181 1906 Bibcode 1906ApJ 23 181L doi 10 1086 141330 a href Template Citation html title Template Citation citation a CS1 maint untitled periodical link Lyman Theodore 1914 An Extension of the Spectrum in the Extreme Ultra Violet Nature 93 2323 241 Bibcode 1914Natur 93 241L doi 10 1038 093241a0 a b c d Wiese W L Fuhr J R 2009 Accurate Atomic Transition Probabilities for Hydrogen Helium and Lithium Journal of Physical and Chemical Reference Data 38 3 565 Bibcode 2009JPCRD 38 565W doi 10 1063 1 3077727 Balmer J J 1885 Notiz uber die Spectrallinien des Wasserstoffs Annalen der Physik 261 5 80 87 Bibcode 1885AnP 261 80B doi 10 1002 andp 18852610506 Paschen Friedrich 1908 Zur Kenntnis ultraroter Linienspektra I Normalwellenlangen bis 27000 A E Annalen der Physik 332 13 537 570 Bibcode 1908AnP 332 537P doi 10 1002 andp 19083321303 archived from the original on 2012 12 17 Brackett Frederick Sumner 1922 Visible and Infra Red Radiation of Hydrogen Astrophysical Journal 56 154 Bibcode 1922ApJ 56 154B doi 10 1086 142697 hdl 2027 uc1 b315747 S2CID 122252244 Pfund A H 1924 The emission of nitrogen and hydrogen in infrared J Opt Soc Am 9 3 193 196 Bibcode 1924JOSA 9 193P doi 10 1364 JOSA 9 000193 a b Kramida A E et al November 2010 A critical compilation of experimental data on spectral lines and energy levels of hydrogen deuterium and tritium Atomic Data and Nuclear Data Tables 96 6 586 644 Bibcode 2010ADNDT 96 586K doi 10 1016 j adt 2010 05 001 Humphreys C J 1953 The Sixth Series in the Spectrum of Atomic Hydrogen Journal of Research of the National Bureau of Standards 50 1 doi 10 6028 jres 050 001 Hansen Peter Strong John 1973 Seventh Series of Atomic Hydrogen Applied Optics 12 2 429 430 Bibcode 1973ApOpt 12 429H doi 10 1364 AO 12 000429 PMID 20125315 Pickering E C 1896 Stars having peculiar spectra New variable stars in Crux and Cygnus Harvard College Observatory Circular 12 1 2 Bibcode 1896HarCi 12 1P Also published as Pickering E C Fleming W P 1896 Stars having peculiar spectra New variable stars in Crux and Cygnus Astrophysical Journal 4 369 370 Bibcode 1896ApJ 4 369P doi 10 1086 140291 Pickering E C 1897 Stars having peculiar spectra New variable Stars in Crux and Cygnus Astronomische Nachrichten 142 6 87 90 Bibcode 1896AN 142 87P doi 10 1002 asna 18971420605 Pickering E C 1897 The spectrum of zeta Puppis Astrophysical Journal 5 92 94 Bibcode 1897ApJ 5 92P doi 10 1086 140312 Fowler A 1912 Observations of the Principal and other Series of Lines in the Spectrum of Hydrogen Monthly Notices of the Royal Astronomical Society 73 2 62 63 Bibcode 1912MNRAS 73 62F doi 10 1093 mnras 73 2 62 Bohr N 1913 The Spectra of Helium and Hydrogen Nature 92 2295 231 232 Bibcode 1913Natur 92 231B doi 10 1038 092231d0 S2CID 11988018 Hoyer Ulrich 1981 Constitution of Atoms and Molecules In Hoyer Ulrich ed Niels Bohr Collected Works Volume 2 Work on Atomic Physics 1912 1917 Amsterdam North Holland Publishing Company pp 103 316 esp pp 116 122 ISBN 978 0720418002 Robotti Nadia 1983 The Spectrum of z Puppis and the Historical Evolution of Empirical Data Historical Studies in the Physical Sciences 14 1 123 145 doi 10 2307 27757527 JSTOR 27757527 External links edit nbsp Media related to Hydrogen spectral series at Wikimedia Commons Retrieved from https en wikipedia org w index php title Hydrogen spectral series amp oldid 1182882861, wikipedia, wiki, book, books, library,

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