The rate of effusion of two gases `a` and `b` under identical conditions of temperature and pressure is in the ratio of 2 : 1. What is the ratio of rms velocity of their molecules if `T_(a)` and `T_(b)` are in the ratio of 2 : 1?

Options

A. `2 : 1`
B. `sqrt2 :1`
C. `2 sqrt2 : 1`
D. `1 : sqrt2`

Answer

C

Explanation

`(r_(a))/(r_(b)) = sqrt((M_(b))/(M_(a))) , (2)/(1) = sqrt((M_(b))/(M_(a))) or (M_(b))/(M_(a)) = (4)/(1)`
`(C_(a))/(C_(b)) = (sqrt((3R T_a)/(M_a)))/(sqrt((3RT_(b))/(M_(b)))) implies (C_(a))/(C_(b)) = sqrt((T_(a)M_(b))/(T_(b)M_(b))) = sqrt((2)/(1) xx (4)/(1))`