The r.m.s velocity of oxygen molecule at $16^{0} C$ is 474m/sec. The r.m.s velocity is m/s of hydrogen molecule at $127^{0} C$

1603

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1896

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2230.59

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2730

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Solution

The correct option is C 2230.59
RMS velocity is given by:
$v_{R M S} = \sqrt{\frac{3 R T}{M}}$
$\frac{v_{h y d r o g e n}}{v_{o x y g e n}} = \sqrt{\frac{M_{o x y g e n} T_{h y d r o g e n}}{M_{h y d r o g e n} T_{o x y g e n}}}$
i.e.
$v_{h y d r o g e n} = v_{o x y g e n} \sqrt{\frac{M_{o x y g e n} T_{h y d r o g e n}}{M_{h y d r o g e n} T_{o x y g e n}}}$
$v_{h y d r o g e n} = 474 \times \sqrt{\frac{32 \times 400}{2 \times 289}} = 2230.5889 m / s$
Hence option C is correct.

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