The time-dependent, mean-field Newns-Anderson model is solved in the wide-band limit. Equations for the time-evolution of the occupation of the spin-dependent adsorbate levels and for the rate of non-adiabatic energy transfer from adsorbate to substrate are derived. Numerical solutions are obtained in the region of space close to the transition point between spin-polarised and non-polarised ground states, for model parameters that correspond to an H-atom incident on the Cu(1 1 1) surface. Away from the spin transition the non-adiabatic energy transfer is in close agreement with the nearly-adiabatic limit. Near the transition, non-adiabatic effects are large and the nearly-adiabatic approximation fails.