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. 1.14
• C. 0.53
• D. 3.96

Answer 1

Answer: (B)

1.14

Answer 2

rms speed $V_{rms} = \sqrt{\frac{V_{1}^{2} + V_{2}^{2} + V_{3}^{2}}{3}}$

$\sqrt{\frac{(0.5)^{2} + (1)^{2} + (2)^{2}}{3}} = 1.3228kms^{- 1}$

Average speed $v_{av} = \frac{v_{1} + v_{2} + v_{3}}{3}$

$= \frac{0.5 + 1 + 2}{3} = 1.17kms^{- 1}$

$= \frac{V_{rms}}{V_{av}} = \frac{1.3228}{1.17} = 1.1306 \cong .14$