Question

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

• A. $80K$
• B. $-73K$
• C. $20K$
• D. $3K$

Answer 1

Answer: (C)

$20K$

RMS velocity of a gas molecule is given by:

$v=\sqrt{\frac{3RT}{M}}$

Let the temperature at which the velocity of hydrogen is equal to the velocity of oxygen at ${47}^{o}C$ be $T$

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

$T=20K$