The rate of effusion of two gases `'a'` and `'b'` under identical conditions of temperature and pressure are 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. `sqrt(2):1`
C. `2sqrt(2):1`
D. `1:sqrt(2)`

Answer

C

Explanation

`(r_(a))/(r_(b))= (2)/(1) =sqrt((M_(b))/(M_(a)))`
`V_(rms) propsqrt((T)/(M))(As V_(rms)=sqrt((3RT)/(M)))`
`(V_(rma)(a))/V_(rms(B))= sqrt((T_(a))/(T_(b))xx(M_(b))/(M_(a)))=(2)/(1)xx(sqrt(2))/(1)= (2sqrt(2))/(1)`
`:. 2sqrt(2):1`