Theories of the Universe: Photoelectric Effect Explained, the Quantum Strikes Again

Photoelectric Effect Explained, the Quantum Strikes Again

Einstein was the first person to take seriously the idea of light quanta and to treat them as more than a mere mathematical trick used to explain the spectrum of black body radiation. Building on Planck's theory, Einstein was able in 1905 to explain another experimental puzzle, the photoelectric effect, by proposing that light is a stream of photon particles, each carrying one quantum of action. His theory that electrons are knocked out of a metal surface (such as zinc or copper plate) by photons, like coconuts being knocked off a fairground shelf by balls, was verified by the appearance of a photographic plate exposed to a very weak beam of light. The plate showed a patchwork of black spots where each photon had knocked out an electron, rather than a uniform gray exposure as would be expected if the light were a series of continuous waves.

Let me present how the photoelectric effect was understood before it was discovered that light also came in chunks of quanta. Then we can see what Einstein discovered and how this revealed that light was a particle and not a wave.

• When you shine ordinary white light on a plate, there is no current. In other words, no electrons are ejected no matter how bright the light.
• If you increase the frequency of the light to a threshold frequency, usually in the ultraviolet, electrons are ejected and current flows.
• When you go above the threshold, the higher the frequency of light, the electrons become more energetic.
• Increasing the brightness of the light does not increase the energy of the electrons. However, it does increase the size of the current.

Are you a little confused? Perhaps rightfully so. But let's go on, I think it will be cleared up soon. For one thing, what we call brightness of a light source is an informal word for its intensity. As you already know, if you increase the intensity of a light source, you increase the energy output. According to Maxwell, the greater the energy in a light wave, the greater the amplitude. So you can think of increasing the intensity as increasing the amplitude of the wave.

But this makes the whole photoelectric effect very mysterious. No matter how much you increase the energy of white light (by increasing the amplitude of the waves), you can't knock any electrons out of the zinc plate. However, if you do increase the frequency, which classically doesn't change the energy of the light, you do knock electrons out. And if you continue to increase the light's frequency, you don't increase the number of electrons knocked out, but you do increase the energy of the electrons. On the other hand, increasing the brightness, which classically does increase the energy of the light, doesn't increase the energy of the electrons, but it does increase the number of ejected electrons. Is this any clearer? Maybe once you see what Einstein did, it'll explain the difference between the classical position and the new quantum.

Einstein explained that by taking the equation at the heart of Planck's description of black body radiation, E = hf, and applying it to electromagnetic radiation, the photoelectric effect could be understood if light itself came in definite chunks, or quanta, each with an energy, hf. It takes one light quantum to knock one electron out of the metal and, for a particular frequency, all the light quanta have the same energy, so all of the liberated electrons have the same energy. In a brighter light of the same color (frequency), there are more light quanta, but each quantum still carries the same energy; so more electrons, still with the same energy, are liberated. And when the frequency is increased, for example from yellow to violet, the frequency is higher, so each light quantum carries more energy, and the liberated electrons move faster, even if only a few electrons are released. Got it?

After that lengthy discussion of the photoelectric effect, I hope you got the gist of the outcome. It boils down to this. The classical understanding of light as a wave couldn't explain why the predictions of how light should behave didn't match the results. Einstein's explanation of light behaving as a particle of energy (light quanta or photon), instead of a wave, produced results that matched predictions. The main problem with this was that it led to the wave/particle duality of light that everyone had a tough time accepting. But in any case, quantum mechanics was starting to take off, and Neils Bohr is our next stop.