The rms velocity of hydrogen is `sqrt7` times the rms velocity of nitrogen If `T` is the temperature of the gas then .

Options

A. `T (He) = T (N_(2))`
B. `T(H_(2)) gt T(N_(2))`
C. `T(H_(2)) lt T(N_(2))`
D. `T(H_(2)) = sqrt7 T (N_(2))`

Answer

C

Explanation

`mu = sqrt((3RT)/(M))`
`(mu_(He))/(mu_(N_(2))) = sqrt((T_(H_(2)))/(M_(H_(2))) xx (M_(N_(2)))/(T_(N_(2))))`
`sqrt7 = sqrt((T_(H_(2)) xx 28)/(T_(N_(2)) xx 2)) = (T_(H) xx 14)/(T_(N_(2)))`
`T_(N_(2)) = 2T_(H_(2)) rArr T_(N_(2)) gt T_(H_(2))`