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This expression is consistent with the integral approximation used in (5.5) and will be used to calculate the quantum number appearing in the partition function (5.7).

        The usual form of the partition function of molecular hydrogen is uH                      = E uR uv                  (5.9)


where

        uE = electronic partition function u R = rotational partition function

        uv = vibrational partition function The electronic partition function is



                    uE =   gj e-Xj/kT               (5.10)
                         J


The statistical weight is given by g. = 2J(j) + 1                                     (5.11)
                     j     H2


where J J) is the total angular momentum of the j-th state
       H2
of H2.

        When the diatomic hydrogen molecule is pictured as a rigid dumbbell with moment of inertia I, rotating in three dimensions, the energy and degeneracy of the J-th