The law of atmospheres states that the number density of molecules in the atmosphere depends on height y above sea level according to
where n0 is the number density at sea level (where y = 0). The average height of a molecule in the Earth’s atmosphere is given by
(a) Prove that this average height is equal to kBT/m0g. (b) Evaluate the average height, assuming the temperature is 10.0°C and the molecular mass is 28.9 u, both uniform throughout the atmosphere.
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