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 pressure

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 molecules
As $PV=k_{B}NT$
$\therefore n=\frac{N}{V}=\frac{P}{k_{B}T}$
$\therefore \lambda =\frac{k_{B}T}{\sqrt{2}\pi d^{2}P}$
where, $k_B=$ Boltzmann constant
$P=$ Pressure of gas
$T=$ Temperature of the gas