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MHT CET 2020 (19 Oct, Shift 2) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from MHT CET 2020 (19 Oct, Shift 2)

Q72MHT CET 2020 · 19 OCT · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

The root mean square velocity of molecules of a gas is $200\text{ m/s}$ . What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

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Answer: (c)

$v_{rms} \propto \sqrt{\frac{T}{M}}$
$T \to \frac{T}{2}$ , $M \to 2M$ : $\frac{T}{M} \to \frac{1}{4}\cdot\frac{T}{M}$ , so $v_{rms}$ halves
$v' = \frac{200}{2} = 100\text{ m/s}$
So the answer is (c) $100\text{ m/s}$ .

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