The ratio between the RMS velocity of `N_(2)` at 200K and that of CO at 800 K is (molecular mass of `N_(1) = 28g mol^(-1)`, molecular mass of `CO = 28g mol^(-1)`)

Options

A. `1.00`
B. 0.75
C. 0.25
D. 0.5

Answer

D

Explanation

RMS velocity `(v_(rms)) = sqrt(3RT//M)`
where, R = molar gas constant
T = temperature in Kelvin
`M_(m)=` molar mass in kilograms/mol `[ :. M_((N_(2))) = M_((CD))]`
`v_(rms) = (N_(2)) = sqrt(3 xx 8.31 xx 200)`
`v_(rms) (CO) = sqrt(3 xx 8.31 xx 800)`
`:. (v_(rms)(N_(2)))/(v_(rms) (CO)) = (sqrt200)/(sqrt800)`
`= (14.14)/(28.28) = 0.50`