The average velocity of gas molecules is 400 `ms^(-1)` . Its r.m.s. velocity at the same temperature is

Options

A. `2.62 ms^(-1)`
B. `1.68 ms^(-1)`
C. `5.86 ms^(-1)`
D. `4.34 ms^(-1)`

Answer

D

Explanation

Average velocity, `u_(av) = sqrt(( 8RT)/( pi M))`
Root mean square velocity, `u _("rms") = sqrt(( 2RT)/( M))`
`(u_(rms))/( u_(av)) = (sqrt((3RT)/( M)))/(sqrt((8RT)/(piM)))`
`= sqrt(( 3pi )/( 8)) = sqrt( ( 3 xx 3.143)/( 8)) = 1.085`
`:. u_("r.m.s.") = 1.805 xx u_(av)`
`= 1.085 xx 400`
`= 4.34 ms^(-1)`