The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room Temperature the rms speed of oxygen molecules is $v$ . The rms speed of the hydrogen molecules at the same temperature will be

v/16

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v/4

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16v

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Solution

The correct option is C
4v

$v = \sqrt{\frac{3 k T}{M}}$ . Therefore, $v_{0} = \sqrt{\frac{3 k T}{M_{0}}}$ and $v_{h} = \sqrt{\frac{3 k T}{M_{h}}}$

Thus, $\frac{v_{0}}{v_{h}} = \frac{M_{h}}{M_{0}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$

Or $v_{h} = 4 v_{0}$

Hence, the correct choice is (c)

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The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room Temperature the rms speed of oxygen molecules is v. The rms speed of the hydrogen molecules at the same temperature will be

The correct option is C 4v v = √3kTM. Therefore, v0 = √3kTM0 and vh = √3kTMh Thus, v0vh = MhM0 = √116 = 14 Or vh = 4v0 Hence, the correct choice is (c)

The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room Temperature the rms speed of oxygen molecules is $v$ . The rms speed of the hydrogen molecules at the same temperature will be

The correct option is C
4v

$v = \sqrt{\frac{3 k T}{M}}$ . Therefore, $v_{0} = \sqrt{\frac{3 k T}{M_{0}}}$ and $v_{h} = \sqrt{\frac{3 k T}{M_{h}}}$

Thus, $\frac{v_{0}}{v_{h}} = \frac{M_{h}}{M_{0}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$

Or $v_{h} = 4 v_{0}$

Hence, the correct choice is (c)