Question

At what temperature is the rms velocity of hydrogen molecule equal to that of an oxygen molecule at $47{}^{\circ }C$?

• A. $10K$
• B. $20K$
• C. $30K$
• D. $40K$

Answer 1

Answer: (B)

$v_{rms}=\sqrt{\frac{3RT}{m}}$
Now, rms velocity of $H_2$ molecule = rms velocity of $O_2$ molecule
$\sqrt{\frac{3R\times T}{2}}=\sqrt{\frac{3R\times \left(47+273\right)}{32}}$
$T=\frac{2\times 320}{32}=20K$