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