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JEE Main 2023 (29 Jan, Shift 2) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from JEE Main 2023 (29 Jan, Shift 2)

Q46JEE Main 2023 · 29 JAN · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

At 300 K, the rms speed of oxygen molecules is α+5α\sqrt{\frac{\alpha+5}{\alpha}} times to that of its average speed in the gas. Then, the value of α\alpha will be

(used π=227\pi = \frac{22}{7})

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Answer: (b)

  1. vrms2vav2=3RT/M8RT/πM=3π8\frac{v_{rms}^2}{v_{av}^2} = \frac{3RT/M}{8RT/\pi M} = \frac{3\pi}{8}
  2. With π=227\pi = \frac{22}{7}: 3π8=3328=28+528\frac{3\pi}{8} = \frac{33}{28} = \frac{28+5}{28}
  3. So α=28\alpha = 28; the answer is (b) 28.
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