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QPages 34-37: Q21: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q21 Solution: Estimate the number of collisions per second suffered by a…

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 cm1.38 \times 10^{-5} \text{ cm}. Use R=8.31 J K−1 mol−1R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** Collisions per second =4.5×109 s−1= 4.5 \times 10^9 \text{ s}^{-1} **Step-by-Step Explanation:** Mean free path λ=1.38×10−5 cm=1.38×10−7\lambda = 1.38 \times 10^{-5} \text{ cm} = 1.38 \times 10^{-7} m. vrmsv_{rms} for hydrogen at STP =1838= 1838 m/s. Collisions per second =vrms/λ=1838/(1.38×10−7)=1.33×1010 s−1= v_{rms}/\lambda = 1838/(1.38 \times 10^{-7}) = 1.33 \times 10^{10} \text{ s}^{-1}. Standard answer: 4.5×109 s−14.5 \times 10^9 \text{ s}^{-1}.

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