First slide

Maxwell speed distribution law

Question

The average speed of molecules of oxygen gas is 450 m/s. If the mean free path is 1.1 × 10^-7 m, then the average number of collisions per second is

Moderate

A

$9 .1 \times 10^{7}$
B

$4 .1 \times 10^{8}$
C

$4 .1 \times 10^{9}$
D

$4 .1 \times 10^{12}$

Solution

$v_{av} = 450 m / s; λ = 1 .1 \times 10^{- 7} m$ .We know that $\bar{λ} = \frac{v_{rms}}{collision frequency}$
$= \frac{v_{av}}{0 .9213 \times collision frequency}$
[Since $v_{av} = 0 .9213 \times v_{rms}$
$1 .1 \times 10^{- 7} = \frac{450}{0 .9213 \times collision frequency}$
Collision frequency $= \frac{450}{0 .9213 \times 1 .1 \times 10^{- 7}}$
$= \frac{450 \times 10^{7}}{0 .9213 \times 1 .1} = 4 .44 \times 10^{9} s^{- 1} ≅ 4 .1 \times 10^{9}$

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