Question
Assume early universe was composed only of Helium instead of Hydrogen.
a) Estimate the temperature of CMB when Helium recombination occurred. Suppose that all the CMB photons have the average energy of the black body spectrum.
b) Repeat your approximation of the temperature, but now assume that you only need 1 photon per Helium atom to keep the atoms ionized. Also suppose fraction of photons with energy greater than E in a black body spectrum is approximately, exp (-E/kT)
c) guess scale factor of the Universe when Helium recombination occurred using your two different answers in part a and b.