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 closest to :

• A. $4.67$
• B. $2.3$
• C. $1.83$
• D. $1.09$

Answer 1

Answer: (D)

$\lambda = \frac{1}{\sqrt{2}\pi n_{v}d^{2}}$
$\tau = \frac{\lambda}{v} = \frac{1}{\sqrt{2}\pi n_{v}d^{2}v}= \frac{1}{\sqrt{2}\pi n_{v}d^{2}}\sqrt{\frac{M}{3RT}}$
$\frac{\tau_{1}}{\tau_{2}} = \sqrt{\frac{M_{1}}{M_{2}}} \frac{d^{2}_{2}}{d^{2}_{1}}$
$= \sqrt{\frac{40}{140}} \frac{\left(0.1\right)^{2}}{\left(0.07\right)^{2}}$
$= 1.09$