Isotopic Effects in Molecular Vibrations

The vibrational wavenumber, a = 2897 cm calculated above is for a H— C1 molecule. But protium, H, is not the only hydrogen isotope found in nature there is deuterium, (D), with a mass equal to two atomic units, and tritium, (T), with atomic mass of 3 amu. The hydrogen atoms found in nature are a mixture of all three isotopes and, like in any mixture, its properties - and mass - are the average value, m(H) = 1.0078 amu. Likewise, chlorine in nature is a mixture of about 75% of isotope C1 and about 25% of isotope C1, so the average mass of Cl atoms is 35.453 amu or that of CI2 molecules twice this. How does this affect molecular vibrations and vibrational spectra  

If you think in terms of large classical bodies - and these are the only bodies that we know of and can think about - then a heavier pendulum will swing slower. The same effect is felt in the atomic world described by the quantum mechanical laws and formulas. The change of vibrational wavenumber in case of atoms of different masses can be calculated using the following equation  

It has been observed and calculated that the force constant (the spring resistance) does not change significantly with smaller changes in mass, the isotopic effect is felt 

Finally, to convert it to conventional vibrational spectroscopic units, cm , you divide this number by 100 [cm- /m ], to get 

The experimentally correct value for the vibration of a sample of natural HCl is 2885.82 cm- so we are 99.97% correct. The vibrational wavenumber, o = 2885 cm is close to but sufficiently different from the one we obtained for the pure C1 isotopic molecule, a = 2897 cm , so in vibrational spectroscopy you have to pay close attention to isotopic masses. Sometimes we use these effects to mark a particular group of atoms by causing a shift in their vibrational wavenumbers. This is done by chemically synthesizing molecules with one kind of isotopes, for example, by preparing H-Cl. This method has been used extensively in the vibrational spectroscopic analysis of larger biological molecules with complicated vibrational spectra. The major instruments used to measure vibrational wavenumbers and strengths are infrared spectrometers and common laboratory infrared spectrometers can detect a difference in one cm better and more expensive instruments go down to 0.025 cm Read the next problem. 

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