0.4 Quantum electron energy levels in an atom  (Page 5/6)

In part (a), we see that, just as expected, a more intense light above the threshold frequency produces more electrons and a greater current. But in part (b), we see that the more intense light above the threshold frequency does not produce electrons with greater kinetic energy. This is not expected, since more energy would have been expected to produce more energetic electrons.

To dig further into these surprising results, let’s fix the intensity of the light and vary the frequency of the source while observing the electric current produced and the kinetic energy of the electrons ejected. The results are also shown in [link] . First, in part (c), we see the threshold frequency clearly. If the frequency is below the threshold frequency, ν ₀ , then no electrons are ejected and there is no current. This suggests that the frequency of the light is related to the energy of the light so that we need a high enough frequency to provide a high enough energy. But part (c) also shows that if the light source is above the threshold, then we get a fixed current, no matter how high the frequency. This also seems strange if the higher frequency light is higher in energy. What happened to the added energy at high frequency? The answer is in part (d), which shows that the kinetic energy of the ejected electrons increases when we increase the frequency of the light source. In fact, it is a very simple relationship. Assuming the frequency is above the threshold, increasing the frequency of the light increases the kinetic energy of the electrons in direct proportion.

To summarize the results in [link] , light which is high intensity but low frequency will not eject electrons. Light which has sufficiently high frequency will eject electrons whether the intensity is low or high. Increasing the intensity gives us more electrons but not more energetic electrons. Increasing the frequency gives us more energetic electrons but not more of them.

This is a very challenging puzzle, and an analogy helps to reveal the subtle answer. Imagine trying to knock pieces out of a wall by throwing objects at it. We discover that, no matter how many ping pong balls we throw, we cannot knock out a piece of the wall. On the other hand, only a single bowling ball is required to accomplish the task. This is because, in either case, the energy from either the ping pong balls or the bowling ball is provided to the wall in individual collisions. Each ball hits the wall individually, whether there are many of them or only one. The key to understanding our imaginary experiment is in discovering that, although there are many more ping-pong balls than bowling balls, it is only the impact of each individual particle with the wall which determines what happens and whether a piece of the wall is knocked loose.

The results of this “experiment” are similar to the observations of the photoelectric effect: very little high frequency light can accomplish what an enormous amount of low frequency light cannot. If we use this analogy, we can reasonably conclude that the energy of the light is supplied in “bundles” or “packets” of constant energy, similar to the energy of the balls being provided in packets. In light, we will call the packets of constant energy “photons.” In the photoelectric effect, each photon or packet of light energy hits the metal surface individually and acts individually.