Question

`v_(rms), v_(av)` and `v_(mp)` are root mean square average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct ?
A. `v_(rms) lt v_(av) lt v_(mp)`
B. `v_(rms) gt v_(av) gt v_(mp)`
C. `v_(mp) lt v_(rms) lt v_(av)`
D. `v_(mp) gt v_(rms) gt v_(av)`

Answer 1

Correct Answer - B
Root mean square speed. The root square speed is used to measure the velocity of particle in a gas. It is given by
`v_(rms) = sqrt((3 RT)/(M)) = 1.732 sqrt((RT)/(M))` …(1)
Where `M` is molar mass and `R` is gas constant, `T` is temperature.
Most probable speed `v_p`, is the speed most likely to be possessed by any molecule in the system.
`v_(av) = sqrt((2RT)/(M)) = 1.41 sqrt((RT)/(M))`...(2)
whereas mean speed is
`v_(mp) = sqrt((8 RT)/(M)) = 1.6 sqrt((RT)/(M))` ...(3)
From Eqs. (1),(2) and (3), we conclude that
`v_(rms) gt v_(av) gt v_(mp)`.