A Variational theory of the radiant emittance of the Mercury-Argon discharge is developed and applied to an investigation of the effects of alterations of the isotopic composition of the Mercury. The theory includes the effects of transport of resonance radiation, elastic and inelastic collisions, resonant exchange of excitation, diffusion of the Mercury atoms, the isotope- and hyperfine-shifted structure of the resonance line, and the surfaces of the discharge on the emittance. Two sensitive parameters - the branching ratio for radiative decay of the resonance state and the rate constant for resonant exchange of excitation - are fitted to data on natural Mercury. The remaining insensitive parameters are given values based on microscopic estimates. The resulting theory reproduces the experimentally observed results for Mercury - 196 enhanced mixtures. We predict small effects for mixtures with othersisotopes enhanced. The crucial role played by resonant exchange of excitation is emphasized.