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	~~Greetings. The author~~'s ~~title is Annabell Traxler~~. ~~Arkansas~~ is ~~wherever her home is. Scheduling vacations is her profession. What her relatives and her really like is fashion and now she has~~ time ~~to just take on new things~~. ~~See what's new on her web-site listed here: http:/~~/[~~http://Www~~.~~google~~.~~de/search?q=jobs.piworld jobs.piworld~~].~~com/NewSite/salomon/zapatillas-salomon-ninos~~.~~cfm<br><br>~~		{{Physical cosmology}}
			In [[cosmology]], '''recombination''' refers to the [[epoch (astronomy)\|epoch]] at which charged [[electron]]s and [[proton]]s first became [[bound state\|bound]] to form [[electric charge\|electrically neutral]] [[hydrogen]] [[atom]]s.<ref group="nb">Note that the term recombination is a [[misnomer]], considering that it represents the ''first'' time that electrically neutral hydrogen formed.</ref> After the [[Big Bang]], the universe was a hot, dense [[plasma (physics)\|plasma]] of [[photon]]s, electrons, and protons. This plasma was effectively opaque to electromagnetic radiation, as the [[Scattering length\|distance]] each photon could travel before encountering a charged particle was very short. As the universe [[Metric expansion of space\|expanded]], it also cooled. Eventually, the universe cooled to the point that the formation of neutral hydrogen was energetically favored, and the fraction of free electrons and protons as compared to neutral hydrogen decreased to about 1 part in 10,000.

	~~Also visit my web site~~ ... [~~http~~://~~Thesaurus~~.~~com~~/~~browse~~/~~Zapatillas Zapatillas~~] ~~Salomon Ni~~& ([http://~~jobs~~.~~piworld~~.com/~~NewSite~~/~~salomon~~/~~zapatillas~~-~~salomon~~-~~ninos~~.~~cfm jobs.piworld~~.com])		Shortly after, photons decoupled from [[matter]] in the universe, which leads to recombination sometimes being called '''photon decoupling''', although recombination and photon decoupling are distinct events. Once photons decoupled from matter, they [[free stream\|traveled freely]] through the universe without interacting with matter, and constitute what we observe today as [[cosmic microwave background radiation]]. Recombination occurred when the universe was roughly 378,000 years old, or at a [[redshift]] of ''z'' = {{val\|1100}}.

			==Derivation of recombination epoch==
			It is possible to find a rough estimate of the redshift of the recombination epoch, starting by considering that during the era preceding recombination, the photons were primarily coupled to matter through the reaction

			:<math>
			H + \gamma \longleftrightarrow p + e^{-}.
			</math><ref>Ryden (2003), p. 156.</ref>

			This reaction requires that the photon (γ) have an energy of at least 13.6 [[electron volt]]s. As long as photons are coupled to matter, this reaction will be in statistical equilibrium, and so the [[Saha equation]] can be applied to determine the equilibrium values of the constituents. This results in the equation

			:<math>
			\frac{n_\text{H}}{n_\text{p} n_\text{e}} = \left(\frac{m_\text{e} k_\text{B} T}{2 \pi \hbar^2}\right)^{-3/2} \exp\left(\frac{Q}{k_\text{B} T}\right),
			</math>

			where ''n'' represents the number density of the subscripted particle, ''m''<sub>e</sub> is the [[electron rest mass\|mass of the electron]], ''k''<sub>B</sub> is [[Boltzmann's constant]], ''T'' is the temperature, ''ħ'' is the [[reduced Planck's constant]], and ''Q'' is the [[binding energy]] of hydrogen.<ref>Ryden (2003), p. 157.</ref> Noting that charge neutrality requires ''n''<sub>e</sub> = ''n''<sub>p</sub>, and then defining the fractional ionization as

			:<math>
			X = \frac{n_\text{p}}{n_\text{p} + n_\text{H}},
			</math><ref name="r153">Ryden (2003), p. 153.</ref>

			the Saha equation can be rewritten as

			:<math>
			\frac{1 - X}{X} = n_\text{p} \left(\frac{m_\text{e} k_\text{B} T}{2 \pi \hbar^2}\right)^{-3/2} \exp\left(\frac{Q}{k_\text{B} T}\right).
			</math><ref name = "r153" />

			The final step is to put this equation in terms of the number density of photons, which is related to the number density of baryons through the baryon-to-photon ratio ''η''. The reason for this is that the baryon-to-photon ratio can be measured, and the number density of photons is given by

			:<math>
			n_\gamma = 0.243\left(\frac{k_\text{B} T}{\hbar c}\right)^3,
			</math>

			where ''c'' is the [[speed of light]]. Then

			:<math>
			\frac{1 - X}{X^2} = 3.84 \eta \left(\frac{k_\text{B} T}{m_\text{e} c^2}\right)^{3/2}\exp\left(\frac{Q}{k_\text{B} T}\right).
			</math><ref>Ryden (2003), p. 158.</ref>

			Solving this equation for a 50 percent ionization yields a recombination temperature of roughly {{val\|4000\|ul=K}}. This, in turn, gives the [[cosmological redshift\|redshift]] as approximately ''z'' = {{val\|1500}}, as the temperature of the radiation in the universe is given by {{nowrap\|1=''T''<sub>r</sub> = 2.728 (1 + z)}}.<ref>Longair (2006), p. 32.</ref> In units of [[Electronvolt#As a unit of temperature\|electronvolt]]s, this temperature is roughly {{val\|0.3\|u=eV}}. This is nearly two [[orders of magnitude]] lower than the [[binding energy]] of [[hydrogen atom\|hydrogen]], which may seem strange, as equilibrium often occurs when the energy scales of two phenomena are roughly equal.<ref>Longair (2006), p. 278.</ref> The reason for the difference is because photons greatly outnumber baryons; the baryon-to-photon ratio is approximately 10<sup>−9</sup>. If there are roughly the same number of photons with an energy greater than the binding energy of hydrogen as there are hydrogen atoms, then the gas will remain ionized. There will be some photons in the [[Wien approximation\|Wien region]] of the black body spectrum with an energy greater than kT, and the number of photons with an energy greater than 13.6 eV does not drop below the number of hydrogen atoms until the temperature is roughly 4000K or 0.3 eV.<ref>Longair (2006), p. 279.</ref> A different statement of this is that recombination was delayed due to the high [[entropy]] of the universe.<ref>Padmanabhan (1993), p. 112.</ref>

			This derivation relied on the assumptions of [[thermodynamic equilibrium]] and recombination directly to the [[ground state]] of hydrogen, each of which simplifies the calculation but also modifies the result. Recombination to an excited state of hydrogen means that recombination proceeds more slowly than that predicted with the Saha equation.<ref>Padmanabhan (1993), pp. 116–117.</ref> A more careful treatment of the physics of recombination yields a value closer to ''z'' = {{val\|1100}}.<ref>Galli ''et al.'' (2008), p.1.</ref>

			==Impact==
			Prior to recombination, photons were not able to freely travel through the universe, as they constantly [[Thomson scattering\|scattered]] off the free electrons and protons. This scattering causes a loss of information, and "there is therefore a photon barrier at a redshift" near that of recombination that prevents us from using photons directly to learn about the universe at larger redshifts.<ref>Longair (2006), p. 280.</ref> Once recombination had occurred, however, the mean free path of photons greatly increased due to the lower number of free electrons. Shortly after recombination, the photon mean free path became larger than the [[Hubble sphere\|Hubble length]], and photons traveled freely without interacting with matter.<ref name="p115">Padmanabhan (1993), p. 115.</ref> For this reason, recombination is closely associated with the last scattering surface, which is the name for the last time at which the photons in the cosmic microwave background interacted with matter.<ref>Longair (2006), p. 281.</ref> However, these two events are distinct, and in a universe with different values for the baryon-to-photon ratio and matter density, recombination and photon decoupling need not have occurred at the same epoch.<ref name="p115"/>

			==See also==
			* [[Timeline of the Big Bang]]
			* [[Chronology of the universe]]
			* [[Big Bang]]

			==Notes==
			{{reflist\|group=nb}}

			==References==
			{{reflist\|2}}

			==Bibliography==
			* {{cite journal \| author = Galli, S.; Bean, R.; Melchiorri, A.; Silk, J. \| title = Delayed recombination and cosmic parameters \| journal = [[Physical Review D]] \| volume = 78 \| issue = 6 \| pages = 063532 \| year = 2008 \| doi = 10.1103/PhysRevD.78.063532 \|arxiv = 0807.1420 \|bibcode= 2008PhRvD..78f3532G}}
			* {{cite book \| last = Longair \| first = Malcolm \| title = Galaxy Formation \| publisher = [[Springer (publisher)\|Springer]] \| year = 2006 \| isbn = 978-3-540-73477-2 \| url = http://books.google.com/?id=blzugw-83nAC}}
			* {{cite book \| last = Padmanabhan \| first = Thanu \| title = Structure formation in the universe \| publisher = [[Cambridge University Press]] \| year = 1993 \| isbn = 0-521-42486-0 \| url = http://books.google.com/?id=AJlOVBRZJtIC}}
			* {{cite book \| last = Ryden \| first = Barbara \| title = Introduction to Cosmology \| publisher = [[Addison-Wesley]] \| year = 2003 \| isbn = 0-8053-8912-1 \| url = http://books.google.com/?id=z27vAAAAMAAJ}}

			{{CMB_experiments}}

			[[Category:Physical cosmology]]

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Greetings. The author's title is Annabell Traxler. Arkansas is wherever her home is. Scheduling vacations is her profession. What her relatives and her really like is fashion and now she has time to just take on new things. See what's new on her web-site listed here: http://[http://Www.google.de/search?q=jobs.piworld jobs.piworld].com/NewSite/salomon/zapatillas-salomon-ninos.cfm<br><br>

Also visit my web site ... [http://Thesaurus.com/browse/Zapatillas Zapatillas] Salomon Ni& ([http://jobs.piworld.com/NewSite/salomon/zapatillas-salomon-ninos.cfm jobs.piworld.com])

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