The problem is that transitions from one s-orbital to another are forbidden, quantum mechanically. There’s no way to emit one photon from an s-orbital and have your electron wind up in a lower energy s-orbital, so the transition we talked about earlier, where you emit a Lyman-series photon, can only occur from the 2 p state to the 1s state.
But there is a special, rare process that can occur: a two-photon transition from the 2s state (or the 3s, or 4s, or even the 3 d orbital) down to the ground (1s) state. It occurs only about 0.000001% as frequently as the Lyman-series transitions, but each occurrence nets us one new neutral hydrogen atom. This quantum mechanical quirk is the primary method of creating neutral hydrogen atoms in the Universe.
If it weren’t for this rare transition, from higher energy spherical orbitals to lower energy spherical orbitals, our Universe would look incredibly different in detail. We would have different numbers and magnitudes of acoustic peaks in the cosmic microwave background, and hence a different set of seed fluctuations for our Universe to build its large-scale structure out of. The ionization history of our Universe would be different; it would take longer for the first stars to form; and the light from the leftover glow of the Big Bang would only take us back to 790,000 years after the Big Bang, rather than the 380,000 years we get today.
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