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Got a question on Cosmology. All the books say decoupling of
radiation from matter took place quite suddenly when the expanding universe
cooled below 3,000-4,000K; at this point the protons captured the
electrons, the hydrogen ceased to be ionized, and neutral hydrogen is much
more transparent. How can this be? kT at 4,000K is only 1/3 eV. With
that little energy, so far below 13.6 eV of the hydrogen ground state, how
could collisions ionize a substantial part of the Hydrogen? If we use the
maxwell-boltzmann relation, only a fraction exp (-13.6/0.333)
= 1.8x10^(-18) of the H-atoms should be ionized, an infinitesimal fraction.
It's hard to believe that only 10^5 free electrons in a mole of atoms
could make the gas opaque to E+M radiation.