Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Estimate the Number of Collisions per Second Suffered by a Molecule in a Sample of Hydrogen at Stp. - Physics

Sum

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.

Use R = 8.31 JK-1 mol-1

#### Solution

Here,

$\lambda = 1 . 38 \times {10}^{- 8} \text { m }$

T = 273 K
M = $2 \times {10}^{- 3} \text{ kg }$

Average speed of the H molecules is given  by

$v_{avg} = \sqrt{\frac{8RT}{\pi M}}$

$= \sqrt{\frac{8 \times 8 . 31 \times 273}{3 . 14 \times 2 \times {10}^{- 3}}}$

$= 1700 \text { ms }^{- 1}$

The time between two collisions is given by

$t = \frac{\lambda}{v_{avg}}$

$\Rightarrow t = \frac{1 . 38 \times {10}^{- 8}}{1700}$

$\Rightarrow t = 8 \times {10}^{- 12} s$

$\text { Number of collisions in 1 s} = \frac{1}{8 . 11 \times {10}^{- 12}} = 1 . 23 \times {10}^{11}$

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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 2 Kinetic Theory of Gases
Q 21 | Page 35