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?

2.15

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1.13

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0.53

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3.96

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Solution

The correct option is C $1.13$
rms speed, $v_{r m s} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + v_{3}^{2}}{3}}$

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

$= 1.32$ km $s^{- 1}$ .

Average speed, $v_{a v} = \frac{v_{1} + v_{2} + v_{3}}{3} = \frac{0.5 + 1 + 2}{3} = 1.17$ km $s^{- 1}$

$= \frac{v_{r m s}}{v_{a v}} = \frac{1.32}{1.17} = 1.13$ .

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