What is the temperature at which oxygen molecules have the same r.m.s velocity as hydrogen molecules
at $27^{\circ}$ C?

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Solution

The correct option is B
$u_{O_{2}} = \sqrt{\frac{3 R T}{32}} [∵ u = \sqrt{\frac{3 R T}{32}}]$
$u_{H_{2}} = \sqrt{\frac{3 R \times 300}{2}}$
But, when $u_{O_{2}} = u_{H_{2}}$
$\sqrt{\frac{3 R T}{32}} = \sqrt{\frac{3 R \times 300}{2}}$
or, $\frac{3 R T}{32} = \frac{3 R \times 300}{2}$
or, $T = \frac{300 \times 32}{2} = 4800 K$
$= (4800 - 273) = 4527^{\circ} C .$

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