Editing Hydrogen line (section)

==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>