level, where J is the rotational quantuma number are (49):


               E(J)= J(J + 1) ( 2/2I)              (5.12)
               rot


               grt- 2J + 1                         (5.13)


The rotational partition function may then be written as


              00       E~(J) A
           1        e (J) -rotk       (2J+1)
      R =     2 rot                   2
          J=0                    J=0


                    x e-J(J+l) (h2/21)/kT          (5.14)
              1
The factor of 1 results from the fact that for a diatomic molecule having similar atoms, only alternate levels can be occupied. In the limit T >> TR, where TR is the temperature equivalent of the energy separation between adjacent rotational states (TR = 851K for H2 (50)), the temperature is high enough to excite many rotational levels. In this case the summation in (5.14) may be replaced by an integral which can be evaluated analytically, giving


   uR JJ( l (h2/2I)/ kT dJ - 4rr2kT I             (5.15)
      0

        The vibrational partition function of a diatomic

molecule is (50)


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