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
• E. independent of temperature

Answer 1

Answer: (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