Verified Solution • 2025–26 Session moderate

QPage 33: Q11: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Page 33: Q11 Solution: The rms speed of oxygen molecules in a gas is . If the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often apply $v_{rms}=\sqrt{3RT/M}$ assuming only temperature changes, forgetting that O$_2$ → 2O halves the molar mass $M$. Since $v\propto\sqrt{T/M}$, doubling $T$ and halving $M$ gives $v' =\sqrt{(2T)/(M/2)}\,v =2v$, not $v\sqrt{2}$.

The rms speed of oxygen molecules in a gas is

v

. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become

Multiple Choice Options

A $v$
B $v\sqrt{2}$
C $2v$
D $4v$

Step-by-Step Verified Solution

**Answer:** (c) 2v. **Step-by-Step Explanation:** v_rms = �(3RT/M). If T is doubled and oxygen molecules dissociate into atoms, M becomes M/2. So v'_rms = �(3R(2T)/(M/2)) = �(4 _ 3RT/M) = 2v.

All Questions in this Chapter

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