Relative densities of H atoms and H/sub 2/(..nu..'') molecules in vibrational levels up to ..nu..'' = 5, effusing from a metal box containing heated tungsten filaments, were detected by a resonance-enhanced multiphoton ionization technique. The atom production is compatible with dissociation of molecules at the filament. The formation of H/sub 2/(..nu..'') is attributed to an Eley-Rideal--type reaction, in which a free atom recombines with an adsorbed atom at the cold wall, followed by desorption. Above 2800 K we observe an abrupt drop in the atom and the H/sub 2/(..nu..'') densities. It is ascribed to the effects of annealing on the filament surface.