A) inversely proportional to number of molecules per unit volume
B) inversely proportional to diameter of the molecule
C) directly proportional to the square root of the absolute temperature
D) directly proportional to the molecular mass
Correct Answer: A
Solution :
: Mean free path,\[\lambda =\frac{1}{\sqrt{2}\pi {{d}^{2}}n}\]where, n = number of molecules per unit volume d = diameter of the molecule As \[PV={{k}_{B}}NT\] \[n=\frac{N}{V}=\frac{P}{{{k}_{B}}T}\therefore \lambda =\frac{{{k}_{B}}T}{\sqrt{2}\pi {{d}^{2}}P}\]where, \[{{k}_{B}}=\]Boltzmann constant P = pressure of gas T = absolute temperature of the gas
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