As a crude approximation, an impurity pentavalent atom in a (tetravalent) silicon lattice...

As a crude approximation, an impurity pentavalent atom in a (tetravalent) silicon lattice can be treated as a one-electron atom, in which the extra electron orbits a net positive charge of I. Because this "atom" is not in free space, however, the permitivity of free space, e0, must be replaced by Kε0, where K is the dielectric constant of the surrounding material. The hydrogen atom ground-state energies would thus become

Given K=12 for silicon, how much energy is needed to free a donor electron in its ground state? (Actually, the effective mass of the donor electron is less than inc, so this prediction is somewhat high.)