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))gtT_(N_(2)`
C. `T_(H_(2))ltT_(N_(2)`
D. `T_(H_(2))=sqrt(7)T_(N_(2)`

Answer

c

Explanation

(c) `U_("rms")=sqrt((3RT)/(Mw))=((U_("rms"))_(H_(2)))/((U_("rms"))_(N_(2)))=sqrt(T_(H_(2))/(M_(H_(2)))xxM_(N_(2))/(T_(N_(2)))),`
`(U_("rms"))_(H_(2))=sqrt(5)(U_("rms"))_(N_(2))`
`:.((U_("rms"))_(H_(2)))/((U_("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)))xx14`
`T_(N_(2))xx5=T_(H_(2))xx14`
`:. " "T_(N_(2))gtT_(H_(2))`