Module 3 : Molecular Spectroscopy
Lecture 13 : Rotational and Vibrational Spectroscopy
  The center of mass is defined by equating the moments on both segments of the molecular axis.
                                                                                                                        (13.1)
  The moment of inertia is defined by
 

                                I  =                                                                                   (13.2)
    =                                                         

                              =                                                                                 (13.3)
 

Since =  ,   r1  =  m2r    Therefore,

           and                                                                           (13.4)

Substituting the above equation in (13.3), we get

                                                                (13.5)

Where μ, the reduced mass is given by

                                                                                                            (13.6)

The rotation of a diatomic is equivalent to a “rotation” of a mass μ at a distance of r from the origin C.  The kinetic energy of this rotational motion is K.E.  =  L2/2I   where L is the angular momentum,  Iω where ω is the angular (rotational) velocity in radians/sec.  The operator for L2 is the same as the operator L2 for the angular momentum of hydrogen atom and the solutions of the operator equations L2 Υlm  =  l (l + 1) Ylm, where Ylm are the spherical harmonics which have been studied in lecture 3.
   
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