THE EFFECTS OF ISOTOPIC SUBSTITUTION

When a specific particular atom in a molecule is replaced by it's isotopes, there no appreciable changes in the intermolecular distances, on isotopic substitution. But there's a changes in total mass hence in the moment of inertia and B value for the molecule.

                    We can consider the two isotopic molecules  ¹²C  ¹⁶O and ¹³C ¹⁶O. There is an increase in mass ¹³C ¹⁶O and hence a decrease in the B value. This changes will be reflected in the rotational energy level of molecules, which is below shown in the figure. The rotational energy levels of ¹³CO are relatively lowered. The rotational constant of ¹²CO and ¹³CO are represented by B and C. The spectrum of the heaviest species will show a smaller separation between the line 2B than that of higher. 

                                 Observation of the decreased separation in rotational lines has led to the evaluation of the accurate atomic weights. In the rotational spectrum of ¹²C and  ¹³CO the values of B and B' are found to be B= 1.92118 cm⁻¹ and B' = 1.83669cm⁻¹

B/B' =    h   *  8π² l' c = l'/l  = μ'/μ

           8π² l꜀      h

B/B' =   1.92118  = 1.046

             1.83669

μ'/μ = 16 × m'  * (12+16) = 1.046

           (16+m')     12× 16

m' = 13.0007

The above the data obtained are natural abundance of   ¹³C   ¹⁶O  i.e  about 1% of ordinary CO molecules. Hence in addition to precise determination of atomic weight, and it's microwave, spectra helps to estimate the natural abundance of isotopes.

Another examples, the microwave spectroscopic observation of ¹⁶OH- ¹⁶OH₂ and its ¹⁸O substituted isotopes forms very small differences (<0.11cm⁻¹) in fitted values of the quenching parameter ρ. The substitution of the water molecule moiety increases ρ, while that on the OH is decreasing it, and the small amount of increasing observed for the doubly substitution from (¹⁸OH− ¹⁸OH₂).