Verified Solution • 2025–26 Session moderate

QPage 33: Q9: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Page 33: Q9 Solution: The rms speed of oxygen at room temperature is about 500 m/s.…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume that the rms speed is directly proportional to the molar mass ($v \propto M$) or inversely proportional to it ($v \propto 1/M$), leading to answers like 31 m/s or 8000 m/s. You must remember that $v_{rms} = \sqrt{3RT/M}$, meaning speed is inversely proportional to the square root of the molar mass ($v \propto 1/\sqrt{M}$), so the ratio of speeds is the square root of the inverse ratio of their masses.

The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about

Multiple Choice Options

  • A 125 m s−1125 \text{ m s}^{-1}
  • B 2000 m s−12000 \text{ m s}^{-1}
  • C 8000 m s−18000 \text{ m s}^{-1}
  • D 31 m s−131 \text{ m s}^{-1}.

Step-by-Step Verified Solution

**Answer:** (b) 2000 m/s. **Step-by-Step Explanation:** v_rms _ 1/�M. For oxygen (M = 32) and hydrogen (M = 2): v_H/v_O = �(32/2) = 4. So v_H = 4 _ 500 = 2000 m/s.

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