energy difference between two states of the atom; we can no longer identify that frequency with a vibration of the atom itself. Nevertheless the concept of the atom as an oscillator does in some respects survive. If the emitted light is analyzed with an interferometer, it is found to consist of wave trains of finite length. The length of the wave trains, divided by c, defines a time t which corresponds to the mean life of the radiating atoms in their excited state, and the surplus energy of a collection of excited atoms decays exponentially as e' (= e') as the energy is radiated away. Neither the photon picture nor the wave picture alone tells us the whole story, but the model of the atom as a damped oscillator provides an acceptable description of some important aspects of the radiative process. As we have seen, the concomitant of a natural frequency of free oscillation is a resonance absorption at about that same frequency. In the case of visible light the frequencies are too high (s 10'Hz) to be measurable, but we are able to describe both emission and absorption in terms of characteristic wavelengths. Probably the most famous example of resonance absorption for light is provided by the Fraunhofer lines. These are the dark lines that are observed in a spectrum analysis of the sun; they are named after Joseph von Fraunhofer, who in a careful study mapped 576 of them in 1814. Figure 4-15(a) shows a portion of