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Interstellar space is pretty empty but there a small number of of atoms (mostly hydrogen?) floating around. How many atoms per light year would a photon encounter while traversing interstellar space?

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check out these lecture slides: – Mark Eichenlaub Nov 14 '10 at 3:08

The number of scattering events ("encounters") per unit path length is equal to the density of scatterers times the scattering cross section (summed over all species of scatterers).

The density of particles (mostly hydrogen atoms) in the interstellar medium (ISM) is on the order of 1/cm^3. If we assume that the photon scattering cross section of a hydrogen atom is the square of a common atomic length scale, 1 angstrom^2, then the number of scattering events per unit path length is 10^-14 per meter, or ~100 per light year, give or take a factor of 10.

Take this with a grain of salt, however! The scattering cross section for photons is strongly energy-dependent. For visible photons, say, the cross section is greatly increased if the photon is sufficiently near an atomic transition energy. The hydrogen atoms "look much larger" to these photons, so there are much more collisions.

Lower in the EM spectrum, you run into the fact that the ISM is actually a plasma (it contains ionized hydrogen and free electrons). I believe the plasma frequency is on the order of 1 kHz (strongly depends on temperature...), so radio waves significantly below 1 kHz cannot propagate through the ISM at all. They scatter from the plasma as a whole, rather than individual particles, so the ISM is actually opaque to them.

So the real answer is "it entirely depends on what energy photons you're talking about".

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What about the density in intergalactic space? – Raskolnikov Nov 14 '10 at 9:30
@Raskolnikov Not my field, but I seem to recall numbers like $1/m^3$ for "local" intergalactic space and much less for the great voids. – dmckee Nov 19 '10 at 3:56

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