It is argued that internal gravity waves generated by the convective envelope of a star may be effective in producing a weak mixing in its radiative interior. The spectrum of wavelengths and frequencies generated is estimated. Only the largest horizontal wavelengths and the lowest frequencies contribute significantly to the wave energy flux and the mixing at the Li-burning depth. At this layer, the combination of the dependence on spectral type, both for the wave energy flux and the shear rate induced by the waves, would produce a distribution of Li abundances similar to that of the Li gap found among F-type stars of several open clusters, and the field. Quantitative agreement with the observed location and time scale of the gap is obtained, but only by increasing the intensity of the waves generated by a factor 15 above straightforward mixing-length estimates. The ratio of mixing length to scale height needed to get the gap in the right spectral range is 1.6. The blue edge of the gap is predicted to be sharp.