The ratio of average speed of an oxygen molecular to the r.m.s. speed of a `N_(2)` molecular at the same temperature is `:`

Options

A. `((3pi )/( 7) )^(1//2)`
B. `(( 7)/( 3pi ))^(1//2)`
C. `((3)/( 7pi ))^(1//2)`
D. `((7pi)/( 3))^(1//2)`

Answer

B

Explanation

`u_(av)` of `O_(2) = sqrt((8RT)/( M)) = sqrt(( 8 RT)/( pi xx 32))`
`u_("rms") ` or `N_(2) = sqrt(( 3RT)/( M)) = sqrt(( 3RT)/( 28))`
`( u_(av))/( u_("rms")) = sqrt((8RT)/(pi xx 32)) xx sqrt((28)/( 3RT)) = (7^(1/2))/( 3pi) `