Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius .1 nm, atomic weight 140) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to :

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1.83

4.67

1.09

2.3

answer is A.

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Detailed Solution

$∴$ $λ = \frac{1}{\sqrt{2} {πn}_{v} d^{2}}$

$τ = \frac{λ}{v} = \frac{1}{\sqrt{2} {πn}_{v} d^{2} v} = \frac{1}{\sqrt{2} {πn}_{v} d^{2}} \sqrt{\frac{M}{3 RT}}$

$\begin{array}{l} \frac{τ_{1}}{τ_{2}} = \sqrt{\frac{M_{1}}{M_{2}}} \frac{d_{2}^{2}}{d_{1}^{2}} = \sqrt{\frac{40}{140}} \frac{(0 .1)^{2}}{(0 .07)^{2}} \\ = 1 .09 \end{array}$

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