Editing Hydrogen line

{{Short description|Spectral line of hydrogen state transition in UHF radio frequencies}}
{{For|hydrogen lines in general|hydrogen spectral series}}
{{Use American English|date = March 2019}}
[[File:Hydrogen-SpinFlip.svg|thumb|A hydrogen atom with proton and electron spins aligned (top) undergoes a flip of the electron spin, resulting in emission of a photon with a 21&nbsp;cm wavelength (bottom)]]

The '''hydrogen line''', '''21&nbsp;centimeter line''', or '''H&nbsp;I line'''{{efn|The "I" in H&nbsp;I is a [[roman numeral]], so it is pronounced "H&nbsp;one". It is also called the "neutral hydrogen" line, with the listener obliged to infer from context that "cold neutral hydrogen" at 1420.4&nbsp;MHz or 0.211&nbsp;m is meant.}} is a [[spectral line]] that is created by a change in the energy state of [[Monatomic gas|solitary]], [[electrically neutral]] [[hydrogen atom]]s. It is produced by a [[Spin (physics)|spin]]-flip transition, which means the direction of the electron's spin is reversed relative to the spin of the proton. This is a [[quantum state]] change between the two [[hyperfine levels]] of the hydrogen [[principal quantum number|1]] [[azimuthal quantum number|s]] [[ground state]]. The [[electromagnetic radiation]] producing this line has a [[frequency]] of {{val|1420.405751768|(2)|ul=MHz}} (1.42&nbsp;GHz),<ref>{{cite journal
 | title=Measurement of the unperturbed hydrogen hyperfine transition frequency
 | last1=Hellwig | first1=Helmut | last2=Vessot | first2=Robert F. C.
 | last3=Levine | first3=Martin W. | last4=Zitzewitz | first4=Paul W.
 | last5=Allan | first5=David W. | last6=Glaze | first6=David J.
 | display-authors=1 | journal=[[List of IEEE publications|IEEE Transactions on Instrumentation and Measurement]]
 | volume=IM-19 | number=4 | page=200 | year=1970
 | doi=10.1109/TIM.1970.4313902 | bibcode=1970ITIM...19..200H
 | url=https://tf.nist.gov/general/pdf/13.pdf | access-date=2023-04-30
}}</ref> which is equivalent to a [[wavelength]] of {{val|21.106114054160|(30)|u=cm|ul=}} in a [[vacuum]]. According to the [[Planck–Einstein relation]] {{math|''E'' {{=}} ''hν''}}, the [[photon]] emitted by this transition has an [[photon energy|energy]] of {{val|5.8743261841116|(81)|u=μ[[electronvolt|eV]]}} [{{val|9.411708152678|(13)|e=−25|u=J}}]. The [[constant of proportionality]], {{mvar|h}}, is known as the [[Planck constant]].

The hydrogen line frequency lies in the [[L band]], which is located in the lower end of the [[microwave]] region of the [[electromagnetic spectrum]]. It is frequently observed in [[radio astronomy]] because those [[radio wave]]s can penetrate the large clouds of interstellar [[cosmic dust]] that are [[opacity (optics)|opaque]] to [[visible light]]. The existence of this line was predicted by Dutch astronomer [[Hendrik van de Hulst|H. van de Hulst]] in 1944, then directly observed by [[Edward Mills Purcell|E. M. Purcell]] and his student [[Harold Irving Ewen|H. I. Ewen]] in 1951. Observations of the hydrogen line have been used to reveal the spiral shape of the [[Milky Way]], to calculate the mass and dynamics of individual galaxies, and to test for changes to the [[fine-structure constant]] over time. It is of particular importance to [[cosmology]] because it can be used to study the early Universe. Due to its fundamental properties, this line is of interest in the [[search for extraterrestrial intelligence]]. This line is the theoretical basis of the [[hydrogen maser]].

==Cause==
{{Further|Hyperfine structure}}
An atom of neutral hydrogen consists of an [[electron]] bound to a [[proton]]. The lowest stationary energy state of the bound electron is called its [[ground state]]. Both the electron and the proton have intrinsic [[magnetic dipole moment]]s ascribed to their [[Spin (physics)|spin]], whose interaction results in a slight increase in energy when the spins are parallel, and a decrease when antiparallel. The fact that only parallel and antiparallel states are allowed is a result of the [[quantum mechanics|quantum mechanical]] discretization of the total [[Angular momentum#Angular momentum in quantum mechanics|angular momentum]] of the system. When the spins are parallel, the magnetic dipole moments are antiparallel (because the electron and proton have opposite charge), thus one would expect this configuration to actually have ''lower energy'' just as two magnets will align so that the north pole of one is closest to the south pole of the other. This logic fails here because the wave functions of the electron and the proton overlap; that is, the electron is not spatially displaced from the proton, but encompasses it. The magnetic dipole moments are therefore best thought of as tiny current loops. As parallel currents attract, the parallel magnetic dipole moments (i.e., antiparallel spins) have lower energy.<ref>{{cite journal |first=D.J. |last=Griffiths |year=1982 |title=Hyperfine splitting in the ground state of hydrogen |journal=[[American Journal of Physics]] |volume=50 |issue=8 |pages=698–703 |doi=10.1119/1.12733 |bibcode = 1982AmJPh..50..698G }}</ref>

In the ground state, the [[Spin transition|spin-flip transition]] between these aligned states has an energy difference of {{val|5.87433|u=μeV}}. When applied to the [[Planck relation]], this gives:

:<math>\lambda = \frac {1}{\nu} \cdot c = \frac {h}{E} \cdot c \approx \frac{\; 4.135\,67 \cdot 10^{-15} \  \mathrm{eV}\cdot\text{s} \;}{5.874\,33 \cdot 10^{-6}\ \mathrm{eV}}\, \cdot\, 2.997\,92 \cdot 10^8 \ \mathrm{m} \cdot \mathrm{s}^{-1} \approx 0.211\,06\ \mathrm{m} = 21.106\ \mathrm{cm}\; </math>

where {{mvar|λ}} is the [[wavelength]] of an emitted photon, {{mvar|ν}} is its [[frequency]], {{mvar|E}} is the photon energy, {{mvar|h}} is the [[Planck constant]], and {{mvar|c}} is the [[speed of light]] in a vacuum. In a laboratory setting, the hydrogen line parameters have been more precisely measured as:
: ''λ'' = {{val|21.106114054160|(30)|u=cm}}
: ''ν'' = {{val|1420405751.768|(2)|u=Hz}}
in a vacuum.<ref name=Mhaske_et_al_2022>{{cite journal
 | title=A Bose horn antenna radio telescope (BHARAT) design for 21 cm hydrogen line experiments for radio astronomy teaching
 | display-authors=1 | last1=Mhaske | first1=Ashish A.
 | last2=Bagchi | first2=Joydeep | last3=Joshi | first3=Bhal Chandra
 | last4=Jacob | first4=Joe | last5=T | first5=Paul K.
 | journal=American Journal of Physics | arxiv=2208.06070 | date=August 2022 | volume=90 | issue=12 | pages=948–960 | doi=10.1119/5.0065381 }}</ref>

This transition is highly [[forbidden line|forbidden]] with an extremely small transition rate of {{val|2.9|e=−15|u=s<sup>−1</sup>}},<ref>{{cite journal |last1=Wiese |first1=W.L. |last2=Fuhr |first2=J.R. |date=2009-06-24 |title=Accurate atomic transition probabilities for hydrogen, helium, and lithium |journal=[[Journal of Physical and Chemical Reference Data]] |volume=38 |issue=3 |pages=565–720 |doi=10.1063/1.3077727 |bibcode=2009JPCRD..38..565W |issn=0047-2689  |url=https://aip.scitation.org/doi/10.1063/1.3077727}}</ref> and a mean lifetime of the excited state of around 11&nbsp;million years.<ref name=Mhaske_et_al_2022/> Collisions of neutral hydrogen atoms with electrons or other atoms can help promote the emission of 21&nbsp;cm photons.<ref>{{cite journal
 | title=The spin temperature of neutral hydrogen during cosmic pre-reionization
 | last=Nusser | first=Adi
 | journal=Monthly Notices of the Royal Astronomical Society
 | volume=359 | issue=1 | pages=183–190
 | date=May 2005 | doi=10.1111/j.1365-2966.2005.08894.x 
 | doi-access=free | arxiv=astro-ph/0409640 | bibcode=2005MNRAS.359..183N
| s2cid=11547883 }}</ref> A spontaneous occurrence of the transition is unlikely to be seen in a laboratory on Earth, but it can be artificially induced through [[stimulated emission]] using a [[hydrogen maser]].<ref>{{cite journal
 | title=The Atomic Hydrogen Maser
 | last=Ramsey | first=Norman F. | author-link=Norman Foster Ramsey Jr.
 | journal=Metrologia | date=January 1965
 | volume=1 | issue=1 | pages=7–15
 | doi=10.1088/0026-1394/1/1/004 | bibcode=1965Metro...1....7R
 | s2cid=250873158 | url=http://www.leapsecond.com/history/1965-Metrologia-v1-n1-Ramsey.pdf
 | access-date=2023-04-27
}}</ref> It is commonly observed in astronomical settings such as [[H I region|hydrogen clouds]] in our galaxy and others. Because of the [[uncertainty principle]], its long lifetime gives the [[spectral line]] an extremely small [[Spectral line#Natural broadening|natural width]], so most broadening is due to [[Doppler shift]]s caused by bulk motion or nonzero temperature of the emitting regions.<ref name=Pritchard_Loeb_2012>{{cite journal
 | title=21 cm cosmology in the 21st century
 | last1=Pritchard | first1=Jonathan R.
 | last2=Loeb | first2=Abraham | author2-link=Avi Loeb
 | journal=Reports on Progress in Physics
 | volume=75 | issue=8 | id=086901
 | date=August 2012 | page=086901 | doi=10.1088/0034-4885/75/8/086901 
 | pmid=22828208 | arxiv=1109.6012 | bibcode=2012RPPh...75h6901P | s2cid=41341641 }}</ref>

==Discovery==
[[File:Green Banks - Ewen-Purcell Horn Antenna.jpg|right|thumb|[[Horn antenna]] used by Ewen and Purcell for the first detection of hydrogen line emission from the [[Milky Way]]]]
During the 1930s, it was noticed that there was a radio "hiss" that varied on a daily cycle and appeared to be extraterrestrial in origin. After initial suggestions that this was due to the Sun, it was observed that the radio waves seemed to propagate from the [[Galactic Center|centre of the Galaxy]]. These discoveries were published in 1940 and were noted by [[Jan Oort]] who knew that significant advances could be made in astronomy if there were [[emission line]]s in the radio part of the spectrum. He referred this to [[Hendrik van de Hulst]] who, in 1944, predicted that [[electric charge|neutral]] [[hydrogen]] could produce radiation at a [[frequency]] of {{val|1420.4058|u=MHz}} due to two closely spaced energy levels in the [[ground state]] of the [[hydrogen atom]].<ref>{{cite journal
 | title=Line Spectra in Radio Astronomy
 | first=E. M. | last=Purcell | author-link=Edward Mills Purcell
 | journal=Proceedings of the American Academy of Arts and Sciences
 | year=1953 | volume=82 | issue=7 | pages=347–349
 | doi=10.2307/20023736 | jstor=20023736 }}</ref>

The 21&nbsp;cm line (1420.4&nbsp;MHz) was first detected in 1951 by [[Harold Irving Ewen|Ewen]] and [[Edward Mills Purcell|Purcell]] at [[Harvard University]],<ref>{{cite journal |last1=Ewen |first1=H.I. |first2=E.M. |last2=Purcell |author2-link=Edward Mills Purcell |date=September 1951 |title=Observation of a line in the galactic radio spectrum: Radiation from galactic hydrogen at 1,420&nbsp;Mc./sec. |journal=[[Nature (journal)|Nature]]|volume=168 |issue=4270 |page=356 |doi=10.1038/168356a0 |bibcode = 1951Natur.168..356E |s2cid=27595927 }}</ref> and published after their data was corroborated by Dutch astronomers Muller and Oort,<ref>{{cite journal |last1=Muller |first1=C.A. |first2=J.H. |last2=Oort |date=September 1951 |title=The interstellar hydrogen line at 1,420&nbsp;Mc./sec., and an estimate of galactic rotation |journal=[[Nature (journal)|Nature]] |volume=168 |issue=4270 |pages=357–358 |doi=10.1038/168357a0 |bibcode = 1951Natur.168..357M |s2cid=32329393 }}</ref> and by [[Wilbur Norman Christiansen|Christiansen]] and Hindman in Australia. After 1952 the first maps of the neutral hydrogen in the Galaxy were made, and revealed for the first time the spiral structure of the [[Milky Way]].<ref>{{cite journal
 | title=The spiral structure of the outer part of the Galactic System derived from the hydrogen emission at 21 cm wavelength
 | display-authors=1 | last1=van de Hulst | first1=H. C.
 | last2=Muller | first2=C. A. | last3=Oort | first3=J. H.
 | journal=Bulletin of the Astronomical Institutes of the Netherlands
 | volume=12 | page=117 | date=May 1954
 | bibcode=1954BAN....12..117V
}}</ref><ref>{{cite journal
 | title=The distribution of atomic hydrogen in the outer parts of the Galactic System
 | last=Westerhout | first=G. | author-link=Gart Westerhout
 | journal=Bulletin of the Astronomical Institutes of the Netherlands
 | volume=13 | page=201 | date=May 1957
 | bibcode=1957BAN....13..201W
}}</ref>

==Uses==
===In radio astronomy===
The 21&nbsp;cm spectral line appears within the [[radio spectrum]] (in the [[L band|L&nbsp;band]] of the [[Ultra high frequency|UHF band]] of the [[microwave window]]). Electromagnetic energy in this range can easily pass through the Earth's atmosphere and be observed from the Earth with little interference.<ref>{{cite book
 | title=The American Practical Navigator: An Epitome of Navigation. 2002 Bicentennial Edition
 | first=Nathaniel | last=Bowditch | author-link=Nathaniel Bowditch
 | publisher=National Imagery and Mapping Agency
 | chapter=10. Radio Waves | page=158 | year=2002
 | chapter-url=https://thenauticalalmanac.com/Bowditch-%20American%20Practical%20Navigator/Chapt-10%20RADIO%20WAVES.pdf
 | access-date=2023-04-28
 | quote="Skywaves are not used in the UHF band because the ionosphere is not sufficiently dense to reflect the waves, which pass through it into space. ... Reception of UHF signals is virtually free from fading and interference from atmospheric noise."
}}</ref> The hydrogen line can readily penetrate clouds of interstellar [[cosmic dust]] that are [[opacity (optics)|opaque]] to [[visible light]].<ref>{{cite book
 | title=The Fullness of Space
 | first=Gareth | last=Wynn-Williams | year=1992
 | page=36 | isbn=9780521426381
 | publisher=Cambridge University Press
 | url=https://books.google.com/books?id=wjxrloC2gyMC&pg=PA36
}}</ref> Assuming that the hydrogen atoms are uniformly distributed throughout the galaxy, each line of sight through the galaxy will reveal a hydrogen line. The only difference between each of these lines is the Doppler shift that each of these lines has. Hence, by assuming [[circular motion]], one can calculate the relative speed of each arm of our galaxy. The [[rotation curve]] of our galaxy has been calculated using the {{Val|21|u=cm}} hydrogen line. It is then possible to use the plot of the rotation curve and the velocity to determine the distance to a certain point within the galaxy. However, a limitation of this method is that departures from circular motion are observed at various scales.<ref>{{cite journal
 | title=The Large-Scale Distribution of Hydrogen in the Galaxy
 | last=Kerr | first=Frank J. | author-link=Frank John Kerr
 | journal=Annual Review of Astronomy and Astrophysics
 | volume=7 | page=39 | year=1969
 | doi=10.1146/annurev.aa.07.090169.000351
 | bibcode=1969ARA&A...7...39K }}</ref>

Hydrogen line observations have been used indirectly to calculate the mass of galaxies,<ref>{{cite journal
 | title=Integral Properties of Spiral and Irregular Galaxies
 | last=Roberts | first=Morton S.
 | journal=Astronomical Journal
 | volume=74 | pages=859–876 | date=September 1969
 | doi=10.1086/110874 | bibcode=1969AJ.....74..859R | doi-access=free }}</ref> to put limits on any changes over time of the [[fine-structure constant]],<ref>{{cite journal
 | title=New limits on the possible variation of physical constants.
 | last1=Drinkwater | first1=M. J. | last2=Webb | first2=J. K–
 | last3=Barrow | first3=J. D. | last4=Flambaum | first4=V. V.
 | journal=Monthly Notices of the Royal Astronomical Society
 | volume=295 | pages=457–462
 | date=April 1998 | issue=2 | doi=10.1046/j.1365-8711.1998.2952457.x 
 | doi-access=free | arxiv=astro-ph/9711290 | bibcode=1998MNRAS.295..457D
| s2cid=5938714 }}</ref> and to study the dynamics of individual galaxies. The [[magnetic field]] strength of [[interstellar space]] can be measured by observing the [[Zeeman effect]] on the 21-cm line; a task that was first accomplished by [[Gerrit L. Verschuur|G. L. Verschuur]] in 1968.<ref>{{cite journal
 | title=Positive Determination of an Interstellar Magnetic Field by Measurement of the Zeeman Splitting of the 21-cm Hydrogen Line
 | last=Verschuur | first=G. L. | date=September 1968
 | journal=Physical Review Letters
 | volume=21 | issue=11 | pages=775–778
 | doi=10.1103/PhysRevLett.21.775 | bibcode=1968PhRvL..21..775V
}}</ref> In theory, it may be possible to search for [[antihydrogen]] atoms by measuring the [[Polarization (physics)|polarization]] of the 21-cm line in an external magnetic field.<ref>{{cite journal
 | title=The 21 cm absorption line profile as a tool for the search for antimatter in the universe
 | last1=Solovyev | first1=Dmitry | last2=Labzowsky | first2=Leonti
 | journal=Progress of Theoretical and Experimental Physics
 | volume=2014 | issue=11 | id=111E016 | date=November 2014
 | pages=111E01 | doi=10.1093/ptep/ptu142 | bibcode=2014PTEP.2014k1E01S 
| doi-access=free }}</ref>

Deuterium has a similar hyperfine spectral line at 91.6 cm (327 MHz), and the relative strength of the 21 cm line to the 91.6 cm line can be used to measure the deuterium-to-hydrogen (D/H) ratio. One group in 2007 reported D/H ratio in the [[galactic anticenter]] to be 21 ± 7 parts per million.<ref>{{Cite journal |last1=Rogers |first1=A. E. E. |last2=Dudevoir |first2=K. A. |last3=Bania |first3=T. M. |date=2007-03-09 |title=Observations of the 327 MHz Deuterium Hyperfine Transition |url=https://iopscience.iop.org/article/10.1086/511978/meta |journal=The Astronomical Journal |language=en |volume=133 |issue=4 |pages=1625–1632 |doi=10.1086/511978 |bibcode=2007AJ....133.1625R |s2cid=15541399 |issn=1538-3881|url-access=subscription }}</ref>

===In cosmology===
The line is of great interest in [[Big Bang]] cosmology because it is the only known way to probe the cosmological "[[Dark Ages (cosmology)|dark ages]]" from [[Recombination (cosmology)|recombination]] (when stable hydrogen atoms first formed) to the [[reionization]] epoch. After including the [[redshift]] range for this period, this line will be observed at frequencies from 200&nbsp;MHz to about 15&nbsp;MHz on Earth.<ref>{{cite journal
 | title=Radio Recombination Lines at Decameter Wavelengths: Prospects for the Future
 | last1=Peters | first1=Wendy M. | last2=Clarke | first2=T.
 | last3=Lazio | first3=J. | last4=Kassim | first4=N.
 | display-authors=1 | journal=Astronomy & Astrophysics
 | volume=525 | id=A128
 | date=January 2011 | doi=10.1051/0004-6361/201014707 
 | arxiv=1010.0292 | bibcode=2011A&A...525A.128P | s2cid=53582482 }}</ref> It potentially has two applications. First, by [[Intensity mapping|mapping the intensity]] of redshifted 21&nbsp;centimeter radiation it can, in principle, provide a very precise picture of the [[matter power spectrum]] in the period after recombination.<ref name=Fialkov_Loeb_2013>{{cite journal
 | title=The 21-cm Signal from the cosmological epoch of recombination
 | last1=Fialkov | first1=A. | last2=Loeb | first2=A.
 | journal=Journal of Cosmology and Astroparticle Physics
 | issue=11 | id=066 | date=November 2013
 | volume=2013 | page=066 | doi=10.1088/1475-7516/2013/11/066 
 | arxiv=1311.4574 | bibcode=2013JCAP...11..066F
| s2cid=250754168 }}</ref> Second, it can provide a picture of how the universe was re‑ionized,<ref name=Mellema_et_al_2006>{{cite journal
 | title=Simulating cosmic reionization at large scales - II. The 21-cm emission features and statistical signals
 | last1=Mellema | first1=Garrelt | last2=Iliev | first2=Ilian T.
 | last3=Pen | first3=Ue-Li | last4=Shapiro | first4=Paul R.
 | journal=Monthly Notices of the Royal Astronomical Society
 | volume=372 | issue=2 | pages=679–692 | display-authors=1
 | date=October 2006 | doi=10.1111/j.1365-2966.2006.10919.x 
 | doi-access=free | arxiv=astro-ph/0603518 | bibcode=2006MNRAS.372..679M
| s2cid=16389221 }}</ref> as neutral hydrogen which has been ionized by radiation from stars or quasars will appear as holes in the 21&nbsp;cm background.<ref>{{cite journal
 | title=Redshifted 21 cm Emission from the Pre-Reionization Era. II. H II Regions around Individual Quasars
 | last1=Kohler | first1=Katharina | last2=Gnedin | first2=Nickolay Y.
 | last3=Miralda-Escudé | first3=Jordi | last4=Shaver | first4=Peter A.
 | display-authors=1 | journal=The Astrophysical Journal
 | volume=633 | issue=2 | pages=552–559
 | date=November 2005 | doi=10.1086/444370 
 | arxiv=astro-ph/0501086 | bibcode=2005ApJ...633..552K | s2cid=15210736 }}</ref><ref name=Pritchard_Loeb_2012/>

However, 21&nbsp;cm observations are very difficult to make. Ground-based experiments to observe the faint signal are plagued by interference from television transmitters and the [[ionosphere]],<ref name=Mellema_et_al_2006/> so they must be made from very secluded sites with care taken to eliminate interference. Space based experiments, including on the far side of the Moon (where they would be sheltered from interference from terrestrial radio signals), have been proposed to compensate for this.<ref>{{cite journal
 | title=Transformative science from the lunar farside: observations of the dark ages and exoplanetary systems at low radio frequencies
 | last=Burns | first=Jack O.
 | journal=Philosophical Transactions of the Royal Society A
 | volume=379 | issue=2188 | id=20190564
 | date=January 2021 | doi=10.1098/rsta.2019.0564 
 | pmid=33222645 | pmc=7739898 | arxiv=2003.06881 | bibcode=2021RSPTA.37990564B }}</ref> Little is known about other foreground effects, such as [[synchrotron radiation|synchrotron emission]] and [[bremsstrahlung|free–free emission]] on the galaxy.<ref>{{cite journal
 | title=21 cm Tomography with Foregrounds
 | last1=Wang | first1=Xiaomin | last2=Tegmark | first2=Max
 | last3=Santos | first3=Mário G. | last4=Knox | first4=Lloyd
 | display-authors=1 | journal=The Astrophysical Journal
 | volume=650 | issue=2 | pages=529–537
 | date=October 2006 | doi=10.1086/506597 
 | arxiv=astro-ph/0501081 | bibcode=2006ApJ...650..529W | s2cid=119595472 }}</ref> Despite these problems, 21&nbsp;cm observations, along with space-based gravitational wave observations, are generally viewed as the next great frontier in observational cosmology, after the [[Cosmic microwave background radiation#Polarization|cosmic microwave background polarization]].<ref>{{cite journal
 | title=Peering into the dark (ages) with low-frequency space interferometers
 | last1=Koopmans | first1=Léon V. E. | last2=Barkana | first2=Rennan
 | last3=Bentum | first3=Mark | last4=Bernardi | first4=Gianni
 | last5=Boonstra | first5=Albert-Jan | last6=Bowman | first6=Judd
 | last7=Burns | first7=Jack | last8=Chen | first8=Xuelei
 | last9=Datta | first9=Abhirup | last10=Falcke | first10=Heino
 | last11=Fialkov | first11=Anastasia | last12=Gehlot | first12=Bharat
 | last13=Gurvits | first13=Leonid | last14=Jelić | first14=Vibor
 | last15=Klein-Wolt | first15=Marc | last16=Lazio | first16=Joseph
 | last17=Meerburg | first17=Daan | last18=Mellema | first18=Garrelt
 | last19=Mertens | first19=Florent | last20=Mesinger | first20=Andrei
 | last21=Offringa | first21=André | last22=Pritchard | first22=Jonathan
 | last23=Semelin | first23=Benoit | last24=Subrahmanyan | first24=Ravi
 | last25=Silk | first25=Joseph | last26=Trott | first26=Cathryn
 | last27=Vedantham | first27=Harish | last28=Verde | first28=Licia
 | last29=Zaroubi | first29=Saleem | last30=Zarka | first30=Philippe
 | display-authors=1 | journal=Experimental Astronomy
 | volume=51 | issue=3 | pages=1641–1676 | date=June 2021
 | doi=10.1007/s10686-021-09743-7 | pmid=34511720 | pmc=8416573 | arxiv=1908.04296 | bibcode=2021ExA....51.1641K }}</ref>

===Relevance to the search for non-human intelligent life===
[[Image:Pioneer plaque hydrogen.svg|thumb|The hyperfine transition of hydrogen, as depicted on the Pioneer and Voyager spacecraft.]]

The [[Pioneer plaque]], attached to the [[Pioneer 10]] and [[Pioneer 11]] spacecraft, portrays the hyperfine transition of neutral hydrogen and used the wavelength as a standard scale of measurement. For example, the height of the woman in the image is displayed as eight times 21&nbsp;cm, or 168&nbsp;cm. Similarly the frequency of the hydrogen spin-flip transition was used for a unit of time in a map to Earth included on the Pioneer plaques and also the [[Voyager 1]] and [[Voyager 2]] probes. On this map, the position of the Sun is portrayed relative to 14&nbsp;[[pulsar]]s whose rotation period circa 1977 is given as a multiple of the frequency of the hydrogen spin-flip transition. It is theorized by the plaque's creators that an advanced civilization would then be able to use the locations of these pulsars to locate the [[Solar System]] at the time the spacecraft were launched.<ref>{{cite web
 | title=The Pioneer Plaque: Science as a Universal Language
 | first=Jake | last=Rosenthal | date=January 20, 2016
 | publisher=The Planetary Society
 | url=https://www.planetary.org/articles/0120-the-pioneer-plaque-science-as-a-universal-language
 | access-date=2023-04-26
}}</ref><ref>{{cite journal
 | title=Introducing Humans to the Extraterrestrials: the Pioneering Missions of the Pioneer and Voyager Probes
 | first=Klara Anna | last=Capova | date=October 18, 2021
 | journal=Frontiers in Human Dynamics
 | volume=3 | publisher=Frontiers Media S.A.
 | doi=10.3389/fhumd.2021.714616 | doi-access=free }}</ref>

The 21&nbsp;cm hydrogen line is considered a favorable frequency by the [[SETI]] program in their search for signals from potential extraterrestrial civilizations. In 1959, Italian physicist [[Giuseppe Cocconi]] and American physicist [[Philip Morrison]] published "Searching for interstellar communications", a paper proposing the 21&nbsp;cm hydrogen line and the potential of microwaves in the search for interstellar communications. According to George Basalla, the paper by Cocconi and Morrison "provided a reasonable theoretical basis" for the then-nascent SETI program.<ref>{{cite book |last=Basalla |first=George |date=2006 |title=Civilized Life in the Universe |publisher=[[Oxford University Press]] |isbn=978-0-19-517181-5 |pages=[https://archive.org/details/civilizedlifeinu0000basa/page/133 133–135] |url=https://archive.org/details/civilizedlifeinu0000basa/page/133 }}</ref> Similarly, [[:ru:Маковецкий, Пётр Васильевич|Pyotr Makovetsky]] proposed SETI use a frequency which is equal to either
:{{0}}{{pi}} × {{val|1420.40575177|u=MHz}} ≈ {{val|4.46233627|u=GHz}}

or
:[[Turn (geometry)|2{{pi}}]] × {{val|1420.40575177|u=MHz}} ≈ {{val|8.92467255|u=GHz}}

Since [[pi|{{pi}}]] is an [[irrational number]], such a frequency could not possibly be produced in a natural way as a [[harmonic]], and would clearly signify its artificial origin. Such a signal would not be overwhelmed by the H&nbsp;I line itself, or by any of its harmonics.<ref>{{cite web |last=Makovetsky |first=P. |title=Смотри в корень |trans-title=Look at the root |language=ru |url=http://n-t.ru/ri/mk/sk109-4.htm}}</ref>

==See also==
{{div col begin |colwidth=15em}}
* [[Balmer series]]
* [[Chronology of the universe]]
* [[Dark Ages Radio Explorer]]
* [[Hydrogen spectral series]]
* [[H-alpha]], the visible red spectral line with wavelength of 656.28&nbsp;[[nanometer]]s
* [[Rydberg formula]]
* [[Timeline of the Big Bang]]
{{div col end}}

==Footnotes==
{{notelist}}

==References==
{{reflist|25em}}

==Further reading==
===Cosmology===
{{div col begin |colwidth=20em}}

* {{cite journal
 |first1=P.   |last1=Madau
 |first2=A.   |last2=Meiksin
 |first3=M.J. |last3=Rees
 |year=1997
 |title=21&nbsp;cm tomography of the intergalactic medium at high redshift
 |journal=[[The Astrophysical Journal]]
 |volume=475  |issue=2  |pages=429–444
 |arxiv=astro-ph/9608010  |doi=10.1086/303549
 |bibcode=1997ApJ...475..429M  |s2cid=118239661
}}

* {{cite journal
 |first1=B.  |last1=Ciardi
 |first2=P.  |last2=Madau
 |year=2003
 |title=Probing beyond the epoch of hydrogen reionization with 21&nbsp;centimeter radiation
 |journal=[[The Astrophysical Journal]]
 |volume=596  |issue=1  |pages=1–8
 |arxiv=astro-ph/0303249  |doi=10.1086/377634
 |bibcode=2003ApJ...596....1C  |s2cid=10258589
}}

* {{cite journal
 |first1=M.  |last1=Zaldarriaga
 |first2=S.  |last2=Furlanetto
 |first3=L.  |last3=Hernquist
 |year=2004
 |title=21&nbsp;centimeter fluctuations from cosmic gas at high redshifts
 |journal=[[The Astrophysical Journal]]
 |volume=608  |issue=2  |pages=622–635
 |arxiv=astro-ph/0311514  |doi=10.1086/386327
 |bibcode=2004ApJ...608..622Z  |s2cid=119439713
}}

* {{cite journal
 |first1=S.  |last1=Furlanetto
 |first2=A.  |last2=Sokasian
 |first3=L.  |last3=Hernquist
 |year=2004
 |title=Observing the reionization epoch through 21&nbsp;centimeter radiation
 |journal=[[Monthly Notices of the Royal Astronomical Society]]
 |volume=347  |issue=1  |pages=187–195
 |arxiv=astro-ph/0305065  |doi=10.1111/j.1365-2966.2004.07187.x
 |doi-access=free
 |bibcode=2004MNRAS.347..187F  |s2cid=6474189
}}

* {{cite journal
 |first1=A.  |last1=Loeb
 |first2=M.  |last2=Zaldarriaga
 |year=2004
 |title=Measuring the small-scale power spectrum of cosmic density fluctuations through 21&nbsp;cm tomography prior to the epoch of structure formation
 |journal=[[Physical Review Letters]]
 |volume=92  |issue=21  |page=211301
 |arxiv=astro-ph/0312134  |doi= 10.1103/PhysRevLett.92.211301
 |pmid=15245272  |bibcode=2004PhRvL..92u1301L  |s2cid=30510359
}}
* {{cite journal
 |first1=M.G. |last1=Santos
 |first2=A.   |last2=Cooray
 |first3=L.   |last3=Knox
 |year=2005
 |title=Multifrequency analysis of 21&nbsp;cm fluctuations from the era of reionization
 |journal=[[The Astrophysical Journal]]
 |volume=625  |issue=2  |pages=575–587
 |arxiv=astro-ph/0408515  |doi=10.1086/429857
 |bibcode=2005ApJ...625..575S  |s2cid=15464776
}}
* {{cite journal
 |first1=R.  |last1=Barkana
 |first2=A.  |last2=Loeb
 |year=2005
 |title=Detecting the earliest galaxies through two new sources of 21&nbsp;cm fluctuations |journal=[[The Astrophysical Journal]]
 |volume=626  |issue=1  |pages=1–11
 |arxiv=astro-ph/0410129  |doi=10.1086/429954
 |bibcode=2005ApJ...626....1B  |s2cid=7343629
}}
* {{cite journal
 |last1=Wang |first1=Jingying           |last2=Xu  |first2=Haiguang
 |last3=An   |first3=Tao                |last4=Gu  |first4=Junhua
 |last5=Guo  |first5=Xueying            |last6=Li  |first6=Weitian
 |last7=Wang |first7=Yu                 |last8=Liu |first8=Chengze
 |last9=Martineau-Huynh |first9=Olivier |last10=Wu |first10=Xiang-Ping
 |date=2013-01-14
 |title=Exploring the cosmic reionization epoch in frequency space: An improved approach to remove the foreground in 21&nbsp;cm tomography
 |journal=[[The Astrophysical Journal]]
 |volume=763  |issue=2  |page=90
 |doi=10.1088/0004-637X/763/2/90  |bibcode=2013ApJ...763...90W
 |issn=0004-637X |arxiv=1211.6450  |s2cid=118712522
}}

{{div col end}}

==External links==
* {{cite web
 |title=The story of Ewen and Purcell's discovery of the 21&nbsp;cm line
 |publisher=[[National Radio Astronomy Observatory]] (NRAO)
 |url=http://www.nrao.edu/whatisra/hist_ewenpurcell.shtml
}}
*  {{cite arXiv
 |author1=Pen, Ue-Li |author2=Wu, Xiang-Ping |author3=Peterson, Jeff
 |date=5 April 2004
 |title=Forecast for Epoch-of-Reionization as viewable by the PrimevAl Structure Telescope (PAST)
 |eprint=astro-ph/0404083
}} — PAST experiment description
* {{cite web
 |title=LOFAR experiment
 |url=http://www.lofar.org/
 |type=main website
}}
* {{cite web
 |title=Mileura Widefield Array experiment
 |url=http://web.haystack.mit.edu/MWA/
 |url-status=dead <!-- presumed -->
 |type=main website
 |archive-url=https://web.archive.org/web/20050211003225/http://web.haystack.mit.edu/MWA/
 |archive-date=2005-02-11
}}
* {{cite web
 |title=Square kilometer array experiment
 |url=http://www.skatelescope.org/
 |type=main website
}}

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