At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$

80K

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– 73K

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20K

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Solution

The correct option is D 20K
${\to C}_{r m s (o)} = {\to C}_{r m s} (H) \sqrt{\frac{3 R T_{0}}{M_{0}}} = \sqrt{\frac{3 R T_{H}}{M_{H}}} ∴ \frac{T_{0}}{M_{0}} = \frac{T_{H}}{M_{H}} ∴ T_{H} = T_{0} . \frac{M_{H}}{M_{0}} = 320 \times \frac{2}{32} = 20 K$

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