On the basis of wave mechanics, it can be seen that if diatomic molecule is considered to be a rigid rotator, i.e., like a rigid dumb bell joined along its line of centers by a bond equal in length the distance r0 between the two nuclei, then the allowed rotational energies of the molecule around the axis passing through the centre of gravity and perpendicular to the line joining the nuclei are given by
                                        
Where J is the rotational quantum number that can have values 0, 1, 2, 3 etc. and I is the moment of inertial of the molecule about the axis of rotation, i.e.
   
                              Rigid rotator.

                     
Where m₁ and m₂ are the atomic masses of the two atoms of the diatomic molecule and
                            
is called the reduced mass.

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