A system consists of two types of gas molecules $A$ and $B$ having same number density $2 \times 10^{25}/\mathrm{m}^{3}$. The diameter of A and B are $10\text{ Å}$ and $5\text{ Å}$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is _____ $\times 10^{-2}$.

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Heat & Thermodynamics

A system consists of two types of gas molecules

A

and

B

having same number density

2 \times 1 0^{25} / m^{3}

. The diameter of A and B are

10 \overset{˚}{A}

and

5 \overset{˚}{A}

respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is _____

\times 1 0^{- 2}

Answer: 25

Solution

The average distance covered between two successive collisions is the mean free path

λ = \frac{1}{2 π d ^{2} n}

Both gases have the same number density, so the mean free path depends only on the molecular diameter,

λ \propto \frac{1}{d ^{2}}

. Hence

\frac{λ _{A}}{λ _{B}} = \frac{d _{B}^{2}}{d _{A}^{2}} = (\frac{5}{10})^{2} = 0.25

The ratio is

25 \times 1 0^{- 2}

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Integer answer

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