question_answer 33)

                  Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters \[1\overset{\text{o}}{\mathop{\text{A}}}\,\] and \[2\overset{\text{o}}{\mathop{\text{A}}}\,\]. The gases may be considered under identical conditions of temperature, pressure and volume.

Answer:

                  Mean free path, \[\lambda =\,\frac{KT}{\sqrt{2}\,\pi \,{{d}^{2}}P}\]                 If P and T are same for all type of molecules.                 \[\lambda \propto \,\frac{1}{{{d}^{2}}}\]                 \[\therefore \] \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}\,=\,{{\left( \frac{{{d}_{ & 2}}}{{{d}_{1}}} \right)}^{2}}\,=4\]