If three gas molecules have velocity `0.5`, `1` and `2 km//s` respectively, find the ratio of their root mean square speed and average speed.

Answer

`1.134`

Explanation

r.m.s. Speed, `C_(rms) = sqrt((C_(1)^(2)+C_(2)^(2)+C_(3)^(2))/(3))`
`sqrt(((0.5)^(2)+(1)^(2)+(2)^(2))/(3)) = 1.3228 km//s`
Average speed, `C_(av) = (C_(1) +C_(2) +C_(3))/(3) = (0.5 +1 +2)/(3)`
`= 1.167 km//s`
`(C_(rms))/(C_(av))= 1.329/1.167 = 1.134`