If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km/s, the root mean square velocity of oxygen at the same condition in km/s is: (a) 1.0 (b) 1.5 (c) 2.0 (d) 0.5

Answer: (d). At the same temperature vrms ∝ 1/√(M). vO₂vH₂ = √(2/32) = 1/4 vO₂ = 2/4 = 0.5 km/s So the answer is (d) 0.5.

If the root mean square velocity of hydrogen molecule at a given… | JEE Main 2024 (1 Feb, Shift 2)

Q25JEE Main 2024 · 1 FEB · SHIFT 2Easy

Molecular Speeds & Maxwell Distribution

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2\text{ km/s}$ , the root mean square velocity of oxygen at the same condition in $\text{km/s}$ is:

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Answer: (d)

At the same temperature $v_{rms} \propto \frac{1}{\sqrt{M}}$ .
$\frac{v_{O_2}}{v_{H_2}} = \sqrt{\frac{2}{32}} = \frac{1}{4}$
$v_{O_2} = \frac{2}{4} = 0.5\text{ km/s}$
So the answer is (d) 0.5.

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