What Redshift Occurs When Photon and Baryon Densities Equalize at Recombination?

[utopiaNow]

Homework Statement

We are to assume the recombination happens at redshift z_{rec} when the number density of photons n_{\gamma}(z_{rec}) capable of ionizing hydrogen is exactly equal to the number density of baryons 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 z_{rec} we have n_{\gamma}(z_{rec}) = n_{b}(z_{rec}).


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 \Omega_{\gamma}E_{bary} \over hf_{mean}\Omega_{bary} = 1

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

Thanks

 

[George Jones]

Forget cosmology for a while.

If E_I is the ionization energy of hydrogen, any photon with energy greater than E_I can ionize hydrogen. Now consider a blackbody at temperature T. What is the number density for photons with energies greater than E_I?