A diffusing gas molecule of sufficiently light mass (e.g. H2and D2) dispersed in sufficiently small cavities of a polymer will posses ground — state quaentization of energy, both in the cavity and in the transition state. Hence one can observe isotope effects in the activation energies for diffusion and permeation and enthalpies of sorption for two isotopic species, providing the mass ratio of the lighter to the heavier is sufficiently small. These isotope effects were determined for four sorts of polymers and were used to estimate parameters involved in the “Free Volume Theory” of gas diffusion through polymers.