The r.m.s. velocity of hydrogen is `sqrt( 7)` times the r.m.s. velocity of nitrogen. If T is the temperature of the gas `:`

Options

A. `T_(N_(2))=T_(H_(2))`
B. `T_(H_(2))=sqrt(7)T_(N_(2))`
C. `T_(N_(2))=2T_(H_(2))`
D. `T_(N_(2))sqrt(7)T_(H_(2))`

Answer

C

Explanation

Consider the rms velocity of nitrogen=x then the rms velocity of nitrogen =x
Then the rms velocity of hydrogen=`sqrt(x)`
rms velocity of gas (C )=`sqrt((3RT)/(M)`
`[(""^(C)N_(2))/(""^(C)N_(2))]=sqrt((""^(T)N_(2))/(""^(T)H_(2))xx(""^(M)H_(2))/(""^(M)N_(2))`
or `[(x)/(sqrt(7)x)]^(2)=[sqrt((""^(T)N_(2))/(""^(T)H_(2))xx(2)/(28))]^(2)`
or `(x^(2))/(7x^(2))=(""^(T)N_(2))/(""^(T)H_(2))xx(1)/(14)` or `(""^(T)H_(2))/(""^(T)H_(2))=(x^(2))/(7x^(2))xx(14)/(1)`
`therefore ""^(T)N_(2)=2T_(H_(2))`