In this article you can find the reason for spontaneous emission.
The excitation of an electron depends of course on the frequency of the photons you shine on the atom. In practice, these photons are wave packets. If we assume the outer electron is excited the photons must have energies that are equal to the difference (of which there are many) of the energy levels of the electron. If we take one frequency (or better said, a wave packet around a mean value for the frequency), associated with the energy difference between the first energy level of the electron and the second (below that energy the photon can't excite the electron), the more photons you shine on the atom, the higher the energy state of the electron (you have to shine them of course at a faster rate than the rate at which they fall back to lower energy levels). So by shining a lot of photons with the just amount of energy, the electron will eventually be knocked off the atom (the spreading of energies becomes less the higher the energy states).
