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JEE Main 2021 (18 Mar, Shift 2) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from JEE Main 2021 (18 Mar, Shift 2)

Q70JEE Main 2021 · 18 MAR · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be:

(Molecular weight of oxygen is 32g/mol; R = 8.3 J K−1{}^{-1} mol−1{}^{-1})

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Answer: (a)

  1. vrms=3RTMv_{rms} = \sqrt{\frac{3RT}{M}}, vav=8RTπMv_{av} = \sqrt{\frac{8RT}{\pi M}}
  2. vrmsvav=3π8\frac{v_{rms}}{v_{av}} = \sqrt{\frac{3\pi}{8}} (independent of TT and MM)
  3. So the answer is (a) 3π8\sqrt{\frac{3\pi}{8}}.
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