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Big Bird

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When I woke up today in the morning, I had the stupid idea of trying to remember some of my knowledge from university. As it turned out, this was easier thought than done, especially given my still drowsy state of mind.

I want to roughly estimate the penetration depth of visible light in air. First obstacle: what should I assume for the absorption cross section? Should I assume for its diameter the wavelength (600 nm on average), or should I rather assume the bond length (~100 pm)? I know that an accurate analysis would have to take into account the details of the interaction, but as I said, I only want a rough estimate (orders of magnitude).

Anyways if I take the bond length (which would be the best case w.r.t. transparency), I arrive at a cross section of order ~10

Next I considered the number of molecules in a cubic meter of air: N=1000 l/(22.4 l/N

Now, this seems to lead to a macroscopic cross section of that cubic meter of air of ~10

What is wrong about my argument? Or can it even be done on this general level of investigation (i.e. without considering absorption levels of molecules)?

I want to roughly estimate the penetration depth of visible light in air. First obstacle: what should I assume for the absorption cross section? Should I assume for its diameter the wavelength (600 nm on average), or should I rather assume the bond length (~100 pm)? I know that an accurate analysis would have to take into account the details of the interaction, but as I said, I only want a rough estimate (orders of magnitude).

Anyways if I take the bond length (which would be the best case w.r.t. transparency), I arrive at a cross section of order ~10

^{-20}m^{2}.Next I considered the number of molecules in a cubic meter of air: N=1000 l/(22.4 l/N

_{A})~50 N_{A}~10^{26}.Now, this seems to lead to a macroscopic cross section of that cubic meter of air of ~10

^{6}m^{2}as opposed to its geometrical cross section of 1m^{2}. That is, the air should be totally opaque already at distances of 1 meter, or the penetration depth would be ~1 micron.What is wrong about my argument? Or can it even be done on this general level of investigation (i.e. without considering absorption levels of molecules)?

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