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Mean Scattering Time of a Molecule

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Show that the mean-scattering time of a molecule travelling at speed v is

tau = 1/n*sigma*v

(see attachment for symbolic equation)

where n is the molecular density and sigma is the collision cross section. Estimate the mean time between collisions of nitrogen molecules at sea level in the Earth's atmosphere assuming they are travelling at their mean speed.

[You may assume nitrogen molecules are spheres of diameter 0.37 nm and the atmosphere is pure nitrogen.]

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