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In Feynman's Lectures on Physics, it says that the diffusion constant for a diffusive gas may be written as

$$D=\frac{1}{3}lv$$

where $D$ is the diffusion constant, $l$ is the mean free path between collisions, and $v$ is the average velocity. Feynman explains everything except the factor of 1/3, which I'm having trouble justifying. Can anyone point out how to rigorously derive the 1/3 factor? I'm interested in diffusion in a 2D system, so I'm wondering if the 1/3 is general, or if in 2D there is instead a factor of 1/2, or something of the sort. Thanks!

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