JEE Main · PhysicsMedium

$If the root mean square speed of hydrogen molecules at a temperature T is v, then the root mean square speed of oxygen molecules at the same temperature is$

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Correct answer: A — $v /4$

Solution

The rms speed is v_{r m s} \propto \frac{1}{M} . Thus, \frac{v _{O_{2}}}{v _{H_{2}}} = \frac{M _{H_{2}}}{M _{O_{2}}} = \frac{2}{32} = \frac{1}{16} = \frac{1}{4} . Therefore, v_{O_{2}} = \frac{v}{4} .