We have measured the initial (clean surface) reflectance of F-2 and O-2 normally incident on Si(100)-2 x 1 and Si(111)-7 x 7 as a function of incident kinetic energy E(i) at different surface temperatures T-s. For O-2, the technique of King and Wells yields the initial sticking probability, S-O, which increases monotonically with E(i) on both surfaces for nearly all E(i) studied. For F-2, the presence of abstractive chemisorption complicates the interpretation of the measurements. We find that the apparent sticking probability of F-2 increases monotonically with E(i) on both Si(100)-2 x 1 and Si(111)-7 x 7, consistent with the idea that F-2 does not undergo precursor-mediated chemisorption on these clean surfaces. Using a crude model, we show that the data obtained with F-2 on Si(111)-7 x 7 are consistent with F-2 abstractive chemisorption dominating for E(i) < 0.1 eV and dissociative chemisorption becoming more probable as E(i) is increased. We find that the apparent initial sticking probability of F-2 depends linearly on the fluorine coverage, which is consistent with a stepwise chemisorption mechanism. For both F-2 and O-2, the sticking increases with T-s for intermediate incident energies (0.1 eV < E(i) < 0.3 eV). The increase with T-s in the case of F-2 is consistent with a surface dynamical effect whereas for O-2 the increase may be explained by the existence of a negative ion-like intermediate state.