Reflection electron energy loss spectra from some insulating materials (CaCO₃, Li₂CO₃, and SiO₂) taken at relatively high incoming electron energies (5–40 keV) are analyzed. Here, one is bulk sensitive and a well-defined onset of inelastic excitations is observed from which one can infer the value of the band gap. An estimate of the band gap was obtained by fitting the spectra with a procedure that includes the recoil shift and recoil broadening affecting these measurements. The width of the elastic peak is directly connected to the mean kinetic energy of the atom in the material (Doppler broadening). The experimentally obtained mean kinetic energies of the O, C, Li, Ca, and Si atoms are compared with the calculated ones, and good agreement is found, especially if the effect of multiple scattering is taken into account. It is demonstrated experimentally that the onset of the inelastic excitation is also affected by Doppler broadening. Aided by this understanding, we can obtain a good fit of the elastic peak and the onset of inelastic excitations. For SiO₂, good agreement is obtained with the well-established value of the band gap (8.9 eV) only if it is assumed that the intensity near the edge scales as (E − E_gap)^1.5. For CaCO₃, the band gap obtained here (7 eV) is about 1 eV larger than the previous experimental value, whereas the value for Li₂CO₃ (7.5 eV) is the first experimental estimate.