A mixture of 2 moles of helium gas (`(atomic mass)=4a.m.u`) and 1 mole of argon gas (`(atomic mass)=40a.m.u`) is kept at 300K in a container. The ratio of the rms speeds `((v_(rms)(helium))/((v_(rms)(argon))` is

Options

A. 0.32
B. 0.45
C. 2.24
D. 3.16

Answer

D

Explanation

Here, `m_(argon) = 40 and m_(helium) = 4`
`(upsilon_(rms)(helium))/(upsilon_(rms)(argon)) = ?`
In any mixture of gases kept at a particular temperature, average translational kinetic energy of each molecules is the same. ltbr. `:. 1/2 m_(argon) xx upsilon_(rms(argon))^(2) = 1/2 m_(helium) xx upsilon_(rms(helium))^(2)`
`(upsilon_(rms)(helium))/(upsilon_(rms)(argon))=sqrt((m_(argon))/(n_(helium))) = sqrt(40/4) = sqrt(10) = 3.16`.