It is shown that inelastic neutron scattering is uniquely suitable to study the surface sites occupied by atomic hydrogen at the surfaces of 2-4-nm platinum particles on hydrogen-containing, high-surface-area carbonaceous support materials. Molecular and atomic hydrogen species can be discriminated under 800-1200 mbar of hydrogen pressure relevant for the operation conditions of fuel cells and other platinum-based catalysts. The distribution of sites suggests that the shape of the particles is intermediate between cubic and cuboctahedral.