In a diatiomic molecule, the rotational energy at a given temperature

Options

A. obeys Maxwell's distribution
B. have the same value for all molecules
C. equals the translational kinetic energy for each molecule
D. is `(2//3)` rd the translational kinetic energy for each molecule

Explanation

Consider a diatomic molecule as shown in the diagram. ltbr. The total energy associated with the molecule is
`E=1/2 mv_(x)^(2) +1/2mv_(y)^(2)+1/2 mv_(z)^(2)+1/2I_(x)omega_(x)^(2)+1/2I_(y)omega_(y)^(2)`
The above expression contains translational kinetic energy `((1)/(2) mv^(2))` corresponding to velocity in each x,y and z- directions as well as rotational KE`((1)/(2) Iomega^(2))` associated with axis of rotations x and y.

The number of independent terms in the above expression is 5.As we can predict velocities of molecules by Maxwell's distribution ,hence the above expression also obeys Maxwell's distribution. `:. 2` rotational and 3 translational energies are associated with each molecule. `:.` Rotational energy at a given temperature is `((2)/(3))` rd of translational KE of each molecule.