The ratio of average speed of an oxygen molecule to the rms speed of a nitrogen molecule at the same temperature is : `((3pi)/(7))^(1/2)`, `((7)/(3pi))^(1/2)`, `((7)/(3pi))^(1/2)`, `((7pi)/(3))^(1/2)`

Options

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

Answer

B

Explanation

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