The root mean square speed of hydrogen is `sqrt(5)` times than that 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)) = sqrt( 7) T_(N_(2))`

Answer

C

Explanation

`V_("rms") = sqrt((3RT)/(M)) = ((V_("rms") )H_(2))/( (V_("rms"))N_(2)) = sqrt((T_(H_(2)))/(M_(H_(2)))xx(M_(N_(2)))/(TN_(2))),`
`(V_("rms"))_(H_(2)) = sqrt( 5) (V_("rms"))N_(2)`
`:. ((V_("rms"))H_(2))/( (V_("rms"))H_(2))xxsqrt(5) =sqrt((T_(H_(2)))/(T_(N_(2)))xx( 28)/( 2))`
`= ( sqrt( 5))/( 1) =sqrt((T_(H_(2)))/(T_(N_(2)))xx14)`
` = 5= ( T_(H_(2)))/(T_(N_(2))) xx 14`
`T_(N_(2)) xx 5 = T_(H_(2)) xx 14 `
`:. T_(N_(2)) gt T_(H_(2))`