We have determined the unoccupied part of the electronic structure of sodium on Cu(111), employing k-resolved inverse photoemission in the isochromat mode. For Na coverages above 0.15 monolayer, an image-potential surface state is observed 2.3 eV above EF. For the completed p(2×2) Na phase at 0.25-monolayer coverage, a pronounced Na 3pz derived feature occurs 0.4 eV above EF, which exhibits a nearly-free-electron-like energy dispersion. For wave vectors k 0.6 A-1, the unoccupied part of the Na 3s band appears close to the Fermi level. We compare our results with recent band-structure calculations for free and adsorbed Na monolayers. © 1991 The American Physical Society.