Question

Mean free path of a gas molecule is

• 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

Answer 1

The Correct Option is A

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 $PV = k_{B}NT$ $n = \frac{N}{V} = \frac{P}{k_{B}T} \quad\therefore \quad\lambda = \frac{1}{\sqrt{2}\pi d^{2} P}$ where, $k_{B} =$ Boltzmann constant $P =$ Pressure of gas $T =$ Absolute temperature of the gas