The dynamic behavior of sodium silicate liquid and glassy structures were investigated by means of molecular dynamic simulations. Particle interactions were modeled using the central force Born-Mayer potential. Simulations were carried out over approximately half a nanosecond. Dynamic susceptibility spectra describing the response of the alkali cations to thermal activation are reported for various temperatures. The diffusion of alkali cations was found to be solid-like, i.e., occurring as sudden jumps separated by long waiting periods, even above the glass transition temperature. The intermediate scattering functions approximately follow a stretched exponential behaviour, with a stretching exponent of 0.8. The characteristic relaxation times for cation motion depend on the probing wave vector according to a power law, with an exponent close to -2.