Question

If three molecules have velocities $0.5\, km\, s^{-1}$, $1\, km \,s^{-1}$ and $2\, km\, s^{-1}$, the ratio of the rms speed and average speed is

• A. $2.15$
• B. $1.13$
• C. $0.53$
• D. $3.96$

Answer 1

Answer: (B)

rms speed, $v_{rms} = \sqrt{\frac{v^{2}_{1}\,+\,v^{2}_{2}\,+\,v^{2}_{3}}{3}}$
$= \sqrt{\frac{\left(0.5\right)^{2} \,+\, \left(1\right)^{2}\, +\, \left(2\right)^{2}}{3}}$
$= 1.32 \,km \,s^{-1}$.
Average speed, $v_{av} = \frac{v_{1}\,+\,v_{2} + v_{3}}{3} = \frac{0.5\,+\,1\,+\,2}{3} = 1.17\,km\,s^{-1 }$
$= \frac{v_{rms}}{v_{av}} = \frac{1.32}{1.17}\approx1.13$