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)) lt sqrt(7)T_(N_(2))`

Answer

3

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)))/(T_(N_(2)))),`
`(V_(rms))H_(2)=sqrt(5)(V_(rms))N_(2)`
`((V_(rms))H_(2))/((V_(rms)N_(2)))xxsqrt(5)=sqrt((T_(H_(2)))/(M_(H_(2)))xx(M_(N_(2)))/(T_(N_(2)))),`
`(sqrt(5))/(1)=sqrt((T_(H_(2)))/(T_(N_(2)))xx14)`
`5=(T_(H_(2)))/(T_(N_(2)))xx14`
`T_(N_(2))xx5=T_(H_(2))xx14`
`T_(N_(2))gtT_(H_(2))`