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If you shine white light through a gas, electrons can absorb sufficiently energetic photons to reach higher excited states. This produces gaps in the spectrum and it's how Helium was discovered. So goes the story.

But an excited electron now exists above a gap in a lower shell. It should fall back down, re-emitting a photon of the same characteristic frequency.

So why doesn't this plug the gaps in the spectrum?

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When the electron falls to its ground state, it will emit the photon in a random direction.This means that the photon might not travel in the direction as the rest of the white light.

In the absorption spectrum of the sun, there will be some photons of the characteristic frequency of helium, but significantly less than the rest of the spectrum, meaning a gap is created.

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    $\begingroup$ Okay, so some other observer will get the photon, but equally likely an atom from another part of the star might randomly emit its photon in our direction. Shouldn't this compensate? If not, why not? $\endgroup$ – spraff Apr 6 '16 at 12:01
  • $\begingroup$ Because around half the photons are directed back into the sun, where they will be scattered off ionised particles and change their energy. Plus in many cases, rather than a single photon of the same energy being emitted, multiple photons of lower energy are as the bound electron cascades back to the ground state. Also, you can get collisional de-excitation of the excited atom without the emission of any photons, although I have no idea whether that makes a significant contribution or not. $\endgroup$ – PhillS Apr 6 '16 at 12:19

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