Within the electroweak minimal model incorporating neutrino electromagnetic form factors an expression for the energy spectrum of electrons knocked out from atoms in inelastic ve scattering is obtained. The differential cross sections of recoil electrons are calculated for the deep bound shells of F-19(9) and Mo-96(42) atoms. It is shown that these spectra differ significantly from the free-scattering case not only at incoming-neutrino energies comparable with the electron binding, but also at energies larger by an order of magnitude. For magnetic scattering, the cross sections for bound electrons are always lower than for free ones, and the recoil spectrum at low kinetic energies does not diverge but is naturally cut off and reaches a plateau. The role of these effects in scattering of reactor nu(e) by atomic electrons is studied.