A system consists of two types of gas molecules A and B having the same number density 2 × 10 ^ 25 m ^ - 3 . The diameter of A and B are 10A and 5A respectively. They suffer collisions at room temperature. The ratio of

Correct answer: 0 ∵ Mean free path λ = 1 2 π d ^ 2 n λ _ 1 λ _ 2 = d _ 2 ^ 2 n _ 2 d _ 1 ^ 2 n _ 1 = ((5)/(10)) ^ 2 = 0 . 25 = 25 × 10 ^ - 2

JEE Main 202125 JulyEvening Shift

JEE Main 2021 · 25 July · Evening Shift · Physics · Kinetic Theory of Gases

A system consists of two types of gas molecules A and B having the...

A system consists of two types of gas molecules

A

and

B

having the same number density

2 \times {10}^{25}{m}^{- 3}

. The diameter of

A

and

B

are

10A

and

5A

respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule

A

to that of

B

between two successive collisions is ___________

\times {10}^{- 2}

$∵$ Mean free path

$\lambda = \dfrac{1}{\sqrt{2}\pi{d}^{2}n}$

$\dfrac{{\lambda}_{1}}{{\lambda}_{2}} = \dfrac{{d}_{2}^{2}{n}_{2}}{{d}_{1}^{2}{n}_{1}}$

$= {\left(\dfrac{5}{10}\right)}^{2} = 0 . 25 = 25 \times {10}^{- 2}$