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Q.

At a given temperature the root mean square velocity of oxygen and hydrogen molecules are in the ratio

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a

1 : 4

b

16 : 1

c

1 : 16

d

4 : 1

answer is D.

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Detailed Solution

$\begin{array}{l} V_{rms} = \sqrt{\frac{3 RT}{M}} (∴ T = cons tant) \\ V_{rms} α \frac{1}{\sqrt{M}} \\ M_{O_{2}} = 32 amu \\ M_{H_{2}} = 2 amu \\ ∴ \frac{V_{O_{2}}}{V_{H_{2}}} = \sqrt{\frac{M_{H_{2}}}{M_{O_{2}}}} = \sqrt{\frac{2}{32}} = \frac{1}{4} \end{array} V_{O} : V_{H} = 1 : 4$

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