Stern-Lindemann formulation

ACS Symposium Series American Chemical Society Washington, DC, 1975. 

Equation (1) Is the first term of a Taylor expansion valid for (6/T) 2rr. For the case of the non-existence of zero point energy, one predicts an isotope effect for the Pb/ ° Pb vapor pressure ratio two orders of magnitude larger than the prediction from Eq. (1) at 600 K. In addition the no zero point energy case predicts the Pb to have the larger vapor pressure at 600 K. 

Stem s estimate of the difference in vapor pressures of Ne and Ne at 24.6 K througih Eq. (1) led to the first separation of isotopes on a macro scale by Keesom and van Dijk ( ). The same theory, without the approximation (6/T) 1, was used by Urey, Brickwedde, and Murphy ( ) to design a Raleigh distillation concentration procedure to enrich HD in H2 five fold above the natural abundance level, which was adequate to demonstrate the existence of a heavy isotope of hydrogen of mass 2. 

It is important to look into the implications of Eq. (1) since the development of the quantum-statistical mechanical theory of Isotope chemistry from 1915 until 1973 centers about the generalization of this equation and the physical interpretation of the various terms in the generalized equations. According to Eq. (1) the difference in vapor pressures of Isotopes is a purely quantum mechanical phenomenon. The vapor pressure ratio approaches the classical limit, high temperature, as t . The mass dependence of the Isotope effect is 6M/M where 6M = M - M. Thus for a unit mass difference in atomic weights of Isotopes of an element, the vapor pressure isotope effect at the same reduced temperature (0/T) falls off as M 2. Interestingly the temperature dependence of In P /P is T 2 not 6X0/T where 6X.0 is the heat of vaporization of the heavy Isotope minus that of the light Isotope at absolute zero. In fact, it is the difference between 6, the difference in heats of vaporization at the temperature T from ( that leads to the T law. 

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