The temperature of a hydrogen and helium mixture is `T = 300 K`. At what value of the molecules velocity `v` will the Maxwell distribution function `F (v)` yield the same magnitude for both gases ?

Explanation

`(v^2)/(v_(P_H)^3) e^(-v^2//v_(P_H)^2) = (v^2)/(v_(P_(H_e))^3) e^(-v^2//v_(P_(H_e))^2)` or `e^(v^2((.^m He)/(2 kT) -(.^m H)/(2 kT)))=((.^mHe)/(.^m H))^(3//2)`
`v^2 = 3kT (1 n^m He//^m H)/(m_(H_e) -m_H)`, Putting the values we get `v = 1.60 km//s`.