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JEE Main 2022 (29 Jul, Shift 2) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from JEE Main 2022 (29 Jul, Shift 2)

Q52JEE Main 2022 · 29 JUL · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

The root mean square speed of smoke particles of mass 5×10−17 kg5 \times 10^{-17}\text{ kg} in their Brownian motion in air at NTP is approximately. [Given k=1.38×10−23 J K−1k = 1.38 \times 10^{-23}\text{ J K}^{-1} ]

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Answer: (c)

  1. vrms=3kTmv_{rms} = \sqrt{\frac{3kT}{m}} with T=273 KT = 273\text{ K} at NTP
  2. vrms=3×1.38×10−23×2735×10−17=2.26×10−4v_{rms} = \sqrt{\frac{3\times1.38\times10^{-23}\times273}{5\times10^{-17}}} = \sqrt{2.26\times10^{-4}}
  3. vrms≈1.5×10−2 m/s=15 mm/sv_{rms} \approx 1.5\times10^{-2}\text{ m/s} = 15\text{ mm/s}
  4. So the answer is (c) 15 mm s−115\text{ mm s}^{-1}.
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