The molecules of a gas `A` travel four times faster than the molecules of gas `B` at same temperature. The ratio of molecular weights `(M_(A)//M_(B))` is

Options

A. 16
B. `1//16`
C. 4
D. `1//4`

Answer

B

Explanation

Since temperature is same, the kinetic energies of two samples of gases A and B will be same.
Now, `v_(A)=4v_(B)`
`therefore(1)/(2)M_(A)(4v_(B))^(2)=(1)/(2)M_(B)v_(B)^(2)`
`(M_(A))/(M_(B))=(1)/(16)`.