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 (H_(2)) = 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

`u = sqrt((3RT)/(M))`
`u(H_(2)) = sqrt((3RT (H_(2)))/(2))`
`u_(N_(2)) = sqrt((RT (N_(2)))/(28))`
`(u(H_(2)))/(u(N_(2))) = sqrt7`
`:. Sqrt7 = sqrt((T(H_(2)))/(2) (28)/(T(N_(2))))`
`7 = (14 xx T(H_(2)))/(T(N_(2)))`
`(1)/(2) = (T(H_(2)))/(T(N_(2)))`
`(T(H_(2)))/(T(N_(2))) lt 1`