Question

If three molecules have velocities $0.5km{s}^{-1}$, $1km{s}^{-1}$ and $2km{s}^{-1}$, 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, $v_{rms}=\sqrt{\frac{v_1^2+v_2^2+v_3^2}{3}}$
$=\sqrt{\frac{{\left(0.5\right)}^2+{\left(1\right)}^2+{\left(2\right)}^2}{3}}$
$=1.32km{s}^{-1}$.
Average speed, $v_{av}=\frac{v_1+v_2+v_3}{3}=\frac{0.5+1+2}{3}=1.17km{s}^{-1}$
$=\frac{v_{rms}}{v_{av}}=\frac{1.32}{1.17}\approx 1.13$