Size dependence of self-diffusivity of monatomic spherical sorbates within zeolite NaY has been investigated at low temperatures. Self-diffusivity, D, exhibits a pronounced maximum when the size of the diffusant is comparable to the void size. The value of D in the anomalous regime is 17 orders of magnitude higher as compared to the linear regime. The implication of these results on separation of mixtures is discussed. Frequency of the recrossing events across the barrier to diffusion and its dependence on the size as revealed by the transmission coefficient are discussed.