Two containers are filled, each with a different gas. Two containers are at the same temperature. Suppose that the molecules weights of the two gases are `M_(A) and M_(B)`. Then the average momenta (in magnitude) of the molecules are related as

Options

A. `P_(A)=P_(B)`
B. `P_(A)=((M_(B))/(M_(A)))P_(B)`
C. `P_(A)=((M_(B))/(M_(A)))^(1//2)`
D. `P_(A)=((M_(A))/(M_(B)))^(1//2)P_(B)`

Answer

D

Explanation

`(P_(A))/(P_(B))=(M_(A)V_(A))/(M_(B)V_(B))=(M_(A))/(M_(B))sqrt(((3RT)/(M_(A)))/((3RT)/(M_(B))))`
`=(M_(A))/(M_(B))xxsqrt((M_(B))/(M_(A)))=sqrt((M_(A))/(M_(B)))`
`P_(A)=sqrt((M_(A))/(M_(B)))`