Q. The rms velocity of gas molecules is $300\ ms^{- 1}$. The rms velocity of molecules of gas with twice the molecular weight and half the absolute temperature is
A) $300\ ms^{- 1}$
B) $600\ ms^{- 1}$
C) $75\ ms^{- 1}$
D) $150\ ms^{- 1}$
Explanation
(d) Root mean square velocity,
$c = \sqrt{\frac{3pV}{M}} = \sqrt{\frac{3RT}{M}}$
$c_{1} = \sqrt{\frac{3R(\frac{T}{2})}{2M}} = \frac{1}{2}\sqrt{\frac{3RT}{M}}$
$= \ \frac{c}{2} = \frac{300}{2} = 150\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.