If the most probable speed of `CO_(2)` at `27^(@)C` is `400ms^(-1)`. The root mean square velocity of `CO_(2)` at the same temperature in `ms^(-1)` is approximately

Options

A. 600
B. 490
C. 267
D. 245

Answer

B

Explanation

Temperatuer `(T )` is same for most probable
velocity `(V_(mp))` and for root mean square velocity
`V_(mp) = 400 ms^(-1)`
`V_(mp) = sqrt((2RT)/(M ) " or " V_(mp)^(2) = (2RT)/(M )`
`M = (2RT)/(V_(mp)^(2)) = (2RT)/((400)^(2))`
On comparing (i ) and (ii) we have
`(2RT)/((400)^(2)) = (3RT)/(v_(mp)^(2))`
`v_(rms) = 1.2247 xx400`