Determine the gas temperature at which
(a) the root mean square velocity of hydrogen molecules exceeds their most probable velocity by `Delta v = 400 m//s` ,
(b) the velocity distribution function `F (v)` for the oxygen molecules will have the maximum value at the velocity `v = 420 m//s`.

Explanation

(a) `v_(rms) = v_p = (sqrt(3) - sqrt(2)) sqrt((k T)/(m)) = Delta v`,
`T = (m)/(k) ((Delta v)/((sqrt(3) - sqrt(2))))^2//K = 384 K`
(b) Clearly `v` is the most probable speed at this temperature. So
`sqrt((2 kT)/(m)) = v` or `T = (mv^2)/(2 k) = 342 K`.