Q. The root mean square speed of the molecules of a diatomic gas is $v.$ When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is
A) $\sqrt{2}v$
B) $v$
C) $2v$
D) $4v$
Explanation
(c) $v_{rms} = \sqrt{\frac{3RT}{M}}.$ According to problem $T$ will become $2T$ and $M$ will becomes $M/2$ so the value of $v_{rms}$ will increase by $\sqrt{4} = 2times,\ i.e.,$ new root mean square velocity will be $2v$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.