Question

The mean free path $\left(\lambda \right)$ of a gas sample is given by:

• A. $\lambda =\sqrt{2\pi {\sigma }^2{N}^{\ast }}$
• B. $\lambda =\frac{1}{\sqrt{2}.\pi {\sigma }^2{N}^{\ast }}$
• C. $\lambda =\sqrt{2\pi u{\sigma }^2{N}^{\ast }}$
• D. None of these

Answer 1

The correct option is B $\lambda =\frac{1}{\sqrt{2}.\pi {\sigma }^2{N}^{\ast }}$

Mean free path, $\lambda =\frac{\text{Average distance travelled per unit time}\left(u_{avg}\right)}{\text{Number of collision made by single molecule in unit time}}$
$\lambda =\frac{u_{avg}}{Z_1}$
$Z_1=\sqrt{2}\pi {\sigma }^2{N}^{\ast }{u}_{avg}$
Formula for mean free path is $\lambda =\frac{1}{\sqrt{2}.\pi {\sigma }^2{N}^{\ast }}$
where, $N^{\ast }$= Number of particles per unit volume
$\sigma$=Collision diameter (2r)