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Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $(V_{rms})$ and choose the correct answer from the options given below:

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$V_{rms} (mono) < V_{rms} (dia) < V_{rms} (poly)$

$V_{rms} (mono) > V_{rms} (dia) > V_{rms} (poly)$

$V_{rms} (dia) < V_{rms} (poly) < V_{rms} (mono)$

$V_{rms} (mono) = V_{rms} (dia) = V_{rms} (poly)$

answer is B.

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Detailed Solution

$ν_{rms} = \sqrt{\frac{3 RT}{M}}$

$∵ M_{Ne} < M_{cl} < {\underset{}{M}}_{\begin{array}{l} uranium \\ hexafloride \end{array}}$

$∴ {(ν_{rms})}_{mono} > {(ν_{rms})}_{Di} > {(ν_{rms})}_{poly}$

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