If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km/s, the root mean square velocity of oxygen at the same condition in km/s is

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Solution

Q.
If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km/s, the root mean square velocity of oxygen at the same condition in km/s is [2024]

1 2.0

2 0.5

3 1.5

4 1.0

Ans.
(2)

$\frac{{(V_{r m s})}_{H_{2}}}{{(V_{r m s})}_{O_{2}}} = \frac{\sqrt{\frac{3 R T}{M_{H_{2}}}}}{\sqrt{\frac{3 R T}{M_{O_{2}}}}}$

$\Rightarrow \frac{2}{{(V_{r m s})}_{O_{2}}} = \sqrt{\frac{M_{O_{2}}}{M_{H_{2}}}} = \sqrt{\frac{32}{2}}$

$\Rightarrow {(V_{r m s})}_{O_{2}} = 0.5$

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