At what temperature will hydrogen molecules have the same root mean square speed as nitrogen molecules at $27^{\circ} C$ ?

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Solution

$\sqrt{\frac{3 R T}{M_{N}}} = \sqrt{\frac{3 R \times 300 M N}{M_{N}}}$

$\frac{T}{M_{H}} = \frac{300}{M_{N}}$

$\frac{T}{2} = \frac{300}{28}$

$T = 21.43$

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