The ratio of the speed of sound in nitrogen gas to that in helium gas at `300 K` is.

Options

A. `sqrt(2//7)`
B. `sqrt(1//7)`
C. `sqrt(3)//5`
D. `sqrt(6//5)`

Answer

A

Explanation

Speed of sound in an ideal gas is given by
`V=sqrt((gammaRT)/M)`
`V prop sqrt((gamma)/M)` [T is same for the gasses]
`(V_(N_(2)))/(V_(He))=sqrt((gamma_(N_(2)))/(gamma_(He))xx(M_(H_(2)))/(M_(N_(2))))=sqrt(((7//5))/((5//3))(4/28)) =sqrt(3)//5`
`gamma_(N_(2))=7//5` (Diatomic)
`gamma_(He)=5//3` (monoatomic)