The recent Bigeleisens Theory of isotope chemistry of the heavy elements is discussed in terms of nuclear charge size and shape variations, mass formula, even-odd and odd-odd effects, magic numbers, nuclear field shift versus resulting contraction or expansion of the s, p, d, and f shells, and corresponding variations of the isotope ionic radii and isotope ionization potentials. The effects of even-odd, odd-odd, magic and doubly magic nuclei, as accompanied by a decrease of the nuclear charge size, are of the same sign at the same orbitals of the outermost electrons. Therefore, these effects alter the chemical equilibria of the isotope exchange in the same direction. An expansion of the nuclear charge distribution, usually associated with the addition of neutrons to a nucleus, causes all the s orbitals, and to a lesser extent all the p½ orbitals, to expand, resulting in a less effective screening of the nucleus. In consequence, the outer d and all the f orbitals become less diffuse, i.e. they contract. The emphasis is given to the uranium isotope chemistry. It is indicated that the uranium ions involved in the Chemex and Asahi technologies must have the outermost electrons on the s or p orbitals in the respective organic or resin phase complexes, and on the f orbitals in the uranium species of the aqueous phase: U3+ - [Rn]5f3 versus U4+ -[Rn]6d17s15f0 for the Chemex cascade solvent extraction, and U4+ - [Rn]5f2 versus O≡U≡O2+-6p6II4 gII4 u[sgrave]2 g[sgrave]2 u5f06d07s0 for the Asahi process, where the complexes adsorbed by the anion exchange resin correspond to the organic phase species. We conlude that the isotope ions of the heavy elements that have the outermost electrons on the d5/2 or f7/2 and f5/2 subshells in the organic phase species and on the s or P½ orbitals in the aqueous phase complexes should display the inverse chemical isotopic effect in comparison with that reported for the chemical uranium enrichment.