  We study the photoelectric effect on the example of a simplified model of an
atom with a single bound state, coupled to the quantized electromagnetic field.
For this model, we show that Einstein's prediction for the photoelectric effect
is qualitatively and quantitatively correct to leading order in the coupling
parameter. More specifically, considering the ionization of the atom by an
incident photon cloud consisting of $N$ photons, we prove that the total
ionized charge is additive in the $N$ involved photons. Furthermore, if the
photon cloud is approaching the atom from a large distance, the kinetic energy
of the ejected electron is shown to be given by the difference of the photon
energy of each single photon in the photon cloud and the ionization energy.
