A bottle contains 1.0 mole He (g) and a second bottle contains 1.0 mole Ar (g) at the same temperature At this temperature the root mean square speed of He is `1477ms^(-1)` and that of Ar is `467 ms^(-1)` What is the ration of the number of He atoms in the first bottle to the number of Ar atoms in the second bottle having these speeds ? Assume that both gases behave ideally .

Explanation

According to Maxwell' s molecular speed distribution
`(n_g)/(sumn_g)prop(1)/(u_(rms))`
`:. U_(rms) prop (sumn_(g))/(n_(g)) prop (N)/(n_(g)) ( :' 1` mole of both gases)
`u_(rms) Ar prop (N)/(n_(Ar)), u_(rms) heprop (N)/(n_(He))`
`:. (n_(He))/(n_(Ar)) = (u_(rmsAr))/(u_(rms)He) = (467)/(1477) = 0.316` .