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Homework Help: Redshift at recombination

  1. Mar 23, 2009 #1
    1. The problem statement, all variables and given/known data

    We are to assume the recombination happens at redshift [tex]z_{rec}[/tex] when the number density of photons [tex] n_{\gamma}(z_{rec}) [/tex] capable of ionizing hydrogen is exactly equal to the number density of baryons [tex] n_{b}(z_{rec}) [/tex]. Use the measured number density of baryons, the temperature of the CMB and the blackbody radiation to find out at what redshift [tex]z_{rec}[/tex] we have [tex] n_{\gamma}(z_{rec}) = n_{b}(z_{rec}). [/tex]

    2. The attempt at a solution
    Sorry I don't have time to write in detail what I have so far. But basically I come down to [tex] \Omega_{\gamma}E_{bary} \over hf_{mean}\Omega_{bary} [/tex] [tex]= 1 [/tex]

    However this doesnt make use of blackbody radation, or the temperature of the CMB, if I'm supposed to equate [tex] \Omega_{\gamma} [/tex] to Temperature of the CMB, then I'm not sure how to do that step.

  2. jcsd
  3. Mar 24, 2009 #2

    George Jones

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    Forget cosmology for a while.

    If [itex]E_I[/itex] is the ionization energy of hydrogen, any photon with energy greater than [itex]E_I[/itex] can ionize hydrogen. Now consider a blackbody at temperature [itex]T[/itex]. What is the number density for photons with energies greater than [itex]E_I[/itex]?
    Last edited: Mar 24, 2009
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