Question

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

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

Answer 1

Answer: (B)

$20 \,K$

Answer 2

$v_{rms} = \sqrt{\frac{3RT}{m}}$ Now, rms velocity of $H_{2}$ molecule = rms velocity of $O_{2}$ molecule $\sqrt{\frac{3R\times T}{2}}= \sqrt{\frac{3R\times\left(47+273\right)}{32}}$ $T = \frac{2\times320}{32} = 20\,K$