The RMS velocity of hydrogen is `sqrt7` times the RMS velocity of nitrogen. If T is the temperature of the gas

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

`rArr (C_(rm s)) H_(2) = sqrt7 (C_(rm s))_(N_(2)) rArr sqrt((cancel(3R)T_(H_(2)))/(2 xx 10^(-3))) = sqrt7 sqrt((cancel(3R)T_(N_(2)))/(28 xx 10^(-3)))`
`rArr (T_(H_(2)))/(1) = 7 xx (T_(N_(2)))/(14) rArr T_(H_(2)) = (T_(N_(2)))/(2) rArr T_(H_(2)) lt T_(N_(2))`