Redshift at recombination
We are to assume the recombination happens at redshift $\displaystyle z_{rec}$ when the number density of photons $\displaystyle n_{\gamma}(z_{rec}) $ capable of ionizing hydrogen is exactly equal to the number density of baryons $\displaystyle n_{b}(z_{rec}) $. Use the measured number density of baryons, the temperature of the CMB and the blackbody radiation to find out at what redshift $\displaystyle z_{rec}$ we have $\displaystyle n_{\gamma}(z_{rec}) = n_{b}(z_{rec}). $
Proposed Solution:
Sorry I don't have time to write in detail what I have so far. But basically I come down to $\displaystyle \Omega_{\gamma}E_{bary} \over hf_{mean}\Omega_{bary} $ $\displaystyle = 1 $
However this doesnt make use of blackbody radation, or the temperature of the CMB, if I'm supposed to equate $\displaystyle \Omega_{\gamma} $ to Temperature of the CMB, then I'm not sure how to do that step.
Thanks
