[en] The F-centre model for the bound state and the first optical transition of an electron in a metal-molten salt solution is examined in the high dilution limit appropriate for comparison with optical absorption data. It is first argued that the model is consistent with recent neutron diffraction and computer simulation data on the structure of pure molten salts, and not incompatible with an Anderson localization model for the electronic conductivity of the solution at higher concentration of metal. A detailed evaluation of the model is presented for the case of a molten salt of equi-sized ions simulating molten KCl. The treatment of the electronic states is patterned after semicontinuum approximations previously applied to the F-centre in ionic crystals, but the equilibrium radius of the electronic cavity and its fluctuations are determined self-consistently from the free energy of the solution. The detailed analysis of this case and the agreement of the results with experiment allow the construction of a simple parametrization scheme, which is then applied to explore the trends of the optical absorption spectrum and of the volume of mixing through the whole family of M-MX solutions, where M is an alkali and X a halogen. Similarities and differences of the electronic bound state in the crystal and in the liquid are underlined. (author)