Here, we report a numerical experiment in which submicrometer particle entrainment in a periodic flow that matches those existing in the alveolus in the human lung was simulated for both sedentary and light activity. A spherical cavity with a prescribed velocity profile at the inlet was used to simulate the time-dependent periodical flow of air in the alveolus. Expansion and contraction of the alveolus were simulated by setting a conceptual permeable wall as the outer surface of the model and adjusting the boundary conditions in order to match the continuity of the flow. The simulations were conducted for breathing periods of 5 and 3 s, which match sedentary and light activity conditions, respectively, and the results were extrapolated to the real lung. It was found that, most of the particles mainly followed a straightforward path and reached the opposite side of the alveolar wall in both breathing conditions. The concentration patterns obtained are consistent with the fact that the flow within the alveolus is mainly diffusive and does not greatly depend on the flow velocity. It was found that the particles which are heavier than air move out of phase with the periodic airflow that crosses the alveolus entrance, and that these particles are significantly caught within the alveolus. Particle entrapment increases with breathing rate in accordance with experimental values and indicates that increase in breathing frequency in environments with high concentration of submicrometer particles has the consequence of increasing particle entrapment by several times with respect to normal breathing rate.