A vessel contains a mixture of one of oxygen and two moles of nitrogen at `300K` The ratio of the average rotational kinetic energy per `O_(2)` molecule to `N_(2)` molecule is .

Options

A. `1 : 2`
B. `2 : 1`
C. `1 : 1`
D. depends upon the moment of inertia of the two molecules

Answer

C

Explanation

Both nitrogen and oxygen molecules are diatomic and they are at the same temperature. Both of them have two rotational degrees of freedom.
The average K.E. per molecule per degree of freedom is `1/2KT`.
`therefore` Both `O_(2) and N_(2)` have the same average rotational K.E. per molecule and is equal to `2xx1/2KT=KT`
`therefore` Their ratio = `1 : 1`