Question

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

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

Answer 1

The correct option is B $20$K

$v_{rms}=\sqrt{\frac{3RT}{M}}$

Now, rms velocity of $H_2$ molecule $=$rms velocity of $O_2$ molecule

$\sqrt{\frac{3R\times T}{2}}=\sqrt{\frac{3R\times (47+273)}{32}}$

$T=\frac{2\times 320}{32}=20$K.