The adsorption of atomic oxygen and nitrogen on the beta-cristobalite (100) surface is investigated from first principles density functional calculations within the generalized gradient approximation. A periodic SiO2 slab model (6 layers relaxing 4 or 6) ended with a layer of Si or O atoms is employed throughout the study. Several adsorption minima and diffusion transition states have been characterized for the two lowest spin states of both systems. A strong chemisorption is found for either O or N in several sites with both slab endings (e.g., it is found an average adsorption energy of 5.89 eV for O (singlet state) and 4.12 eV for N (doublet state) over the Si face). The approach of O or N on top O gives place to the O2 and NO abstraction reactions without energy barriers. Atomic sticking coefficients and desorption rate constants have been estimated (300-1900 K) by using the standard transition state theory. The high adsorption energies found for O and N over silica point out that the atomic recombination processes (i.e., Eley-Rideal and Langmuir-Hinshelwood mechanisms) will play a more important role in the atomic detachment processes than the thermal desorption processes. Furthermore, the different behavior observed for the O and N thermal desorption processes suggests that the published kinetic models for atomic O and N recombination reactions on SiO2 surfaces, based on low adsorption energies (e.g., 3.5 eV for both O and N), should probably be revised.