Two gases-argon (atomic radius 0.07 nm , atomic weight 40) and xenon (atomic radius 0.1 nm, atomic w

Question

Two gases-argon (atomic radius 0.07 nm , atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closed to\

Professor PC Thomas Classes · Answer

(*) : Mean free time of molecules ( $	au$ )\ $=\frac{	ext { mean free path }(\lambda)}{	ext { average speed }(v)}$\ or $\quad 	au=\frac{1}{\sqrt{2} \pi d^{2} n} \frac{1}{\sqrt{8 k T / \pi m}}=\frac{1}{4 d^{2} n} \sqrt{\frac{m}{k T \pi}}$\ Ratio, $\frac{	au_{1}}{	au_{2}}=\frac{\sqrt{m_{1}} / d_{1}^{2}}{\sqrt{m_{2}} / d_{2}^{2}}$\ or $\frac{	au_{1}}{	au_{2}}=\sqrt{\frac{40}{140}}\left(\frac{0.1}{0.07}ight)^{2}=1.09$\ *None of the given options is correct.\