If the r.m.s speed of oxygen at room temperature is √(56) m/s. The r.m.s speed of nitrogen at the same temperature is ________. (a) 8√(2) m/s (b) 8 m/s (c) 16 m/s (d) 7 m/s

Answer: (b). At the same temperature vrms ∝ 1/√(M); MO₂ = 32, MN₂ = 28. vN₂ = √(56) × √(32/28) = √((56 × 32)/(28)) = √(64) vN₂ = 8 m/s So the answer is (b) 8 m/s.

If the r.m.s speed of oxygen at room temperature is √(56) m/s. The… | JEE Main 2022 (30 Jul, Shift 2)

Q49JEE Main 2022 · 30 JUL · SHIFT 2Easy

Molecular Speeds & Maxwell Distribution

If the r.m.s speed of oxygen at room temperature is $\sqrt{56}\text{ m/s}$ . The r.m.s speed of nitrogen at the same temperature is ________.

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Answer: (b)

At the same temperature $v_{rms} \propto \frac{1}{\sqrt{M}}$ ; $M_{O_2} = 32$ , $M_{N_2} = 28$ .
$v_{N_2} = \sqrt{56} \times \sqrt{\frac{32}{28}} = \sqrt{\frac{56 \times 32}{28}} = \sqrt{64}$
$v_{N_2} = 8\text{ m/s}$
So the answer is (b) $8\text{ m/s}$ .

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