Refractive index isotope effects

In the equation s is the measured dielectric constant and e0 the permittivity of the vacuum, M is the molar mass and p the molecular density, while Aa and A (po2) are the isotope effects on the polarizability and the square of the permanent dipole moment respectively. Unfortunately, because the isotope effects under discussion are small, and high precision in measurements of bulk phase polarization is difficult to achieve, this approach has fallen into disfavor and now is only rarely used. Polarizability isotope effects, Aa, are better determined by measuring the frequency dependence of the refractive index (see below), and isotope effects on permanent dipole moments with spectroscopic experiments. 

Here, A and v 2 are fitting parameters amenable to physical interpretation using Equation 12.11. The point of present concern is that the isotope effect on polarizability can now be expressed in terms of isotopic differences in refractive index. It follows from Equation 12.14 that a plot of AR/R = [6n2/((n2—l)(n2 + 2))][An/n] vs. v2 gives an approximately straight line,... 

Using Equation 12.12 one obtains (AA/A — Av /v 2) = (Aao/ao). We see that precise refractive index differences measured over a reasonable range of wavelengths allow the recovery of the polarizability isotope effect (i.e. the isotope effect on the electric field induced dipole moment), provided the molar volume and its isotope effect are available. 

Analysis. There are five important methods for measuring the ratios of isotopes, making use respectively of—the spectrograph, the mass spectrograph, density measurements, atomic weight measurements and refractive index measurements. Any of these methods must be pushed to the present limits of accuracy or beyond in order to meet the requirements for tracer experiments. If, for example, an increase in concentration of C13 is effected from 1 per cent to 1.1 per cent and an accuracy of five per cent in the increase is required the determination must be accurate to one part in 20,000. 

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