Question

Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) = 1.38 × 10⁻⁵ cm.

Answer 1

Here,
$\lambda =1.38\times {10}^{-8}\mathrm{m}$
T = 273 K
M = $2\times {10}^{-3}\mathrm{kg}$

Average speed of the H molecules is given by

$$\begin{gathered} v_{avg}=\sqrt{\frac{8RT}{\mathrm{\pi M}}} \\ =\sqrt{\frac{8\times 8.31\times 273}{3.14\times 2\times {10}^{-3}}} \\ =1700m{s}^{-1} \end{gathered}$$

The time between two collisions is given by

$$\begin{gathered} t=\frac{\lambda }{v_{avg}} \\ \Rightarrow t=\frac{1.38\times {10}^{-8}}{1700} \\ \Rightarrow t=8\times {10}^{-12}s \\ \mathrm{Number}\mathrm{of}\mathrm{collisions}\mathrm{in}1\mathrm{s}=\frac{1}{8.11\times {10}^{-12}}=1.23\times {10}^{11} \end{gathered}$$