Q64 / 75 · JEE Main 2020 (09 Jan Shift 2) · Physics

Two gases - argon (atomic radius $0.07 n m,$ atomic weight $40$ ) and xenon (atomic radius $0.1 n m,$ 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
$3.67$
Correct answer
B
$1.83$
C
$2.3$
D
$4.67$

Solution

Mean free time

= \frac{1}{\sqrt{2} n π d^{2} v_{r m s}}

\frac{t_{A r}}{t_{X e}} = \frac{d_{X e}^{2}}{d_{A r}^{2}} \times \sqrt{\frac{m_{1}}{m_{2}}}

= {(\frac{0.1}{0.07})}^{2} \times \sqrt{\frac{40}{140}}

= {(\frac{10}{7})}^{2} \times \sqrt{\frac{2}{7}} = 1.09

closest value is

1.83

Hence, the correct answer is option: 'B'.

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