Bit By Bit

6 May 2015

The photoelectric effect is used in solar panels. Wikimedia
The photoelectric effect is used in solar panels.

Light is an electromagnetic wave. This was shown definitively when James Clerk Maxwell unified electricity, magnetism and light into a single theory of electromagnetism in the 1860s. By the early 1900s the wave nature of light had been confirmed in numerous ways, from Young’s double slit experiment to diffraction gratings. But there were some phenomena that didn’t quite make sense under the wave model of light, such as the photoelectric effect.

In the late 1800s it was noticed that when a charged metal plate was illuminated by ultraviolet light it would begin to emit electrons. At the time it was thought that this photoelectric effect was due to the electromagnetic waves of ultraviolet light shaking electrons out of the metal, but when the effect was studied in detail that didn’t seem to add up.

Waves can be defined by their frequency (how quickly the waves oscillate) and their amplitude (how large each wave is). The energy of a wave depends upon its amplitude, which for light is related to its brightness. This means that brighter light should cause the released electrons to have have more energy (since brighter light has more energy to give) and dimmer light should give them less energy. In other words, the energy of the electrons should depend on the amplitude of the light.

But experiments showed that the energy depended upon the frequency. The energy of electrons released under a particular a particular frequency of ultraviolet light was always the same. Increasing or decreasing the intensity of the light increased or decreased the number of electrons emitted, but not their individual energies. However if a different color (frequency) of light on the metal, the emitted electrons would have a different energy. The lower the frequency, the lower the electron energy. What made things more strange was that there was a minimum frequency below which no electrons would be released at all. For example, with red light no electrons would be released from the metal, no matter how bright the red light was. On the other hand, very faint ultraviolet light (which has very little energy) would trigger the release of a few electrons.

You can see how odd this is if you imagine the electrons to be like ping pong balls scattered along a beach. The waves of light are then like the waves of the ocean, which can wash the ping pong balls into the sea (like causing the release of electrons from the metal). Now imagine that a very large but slow wave washes onto the shore, but all the ping pong balls stay on the shore. On the other hand, a tiny but quick wave washes along the shore, and a couple of ping pong balls wash into the sea. It makes no sense that the little wave can do what the large wave cannot.

Einstein resolved this problem by proposing that light is not just a wave. In “On a Heuristic Point of View about the Creation and Conversion of Light” he drew upon earlier work by Max Planck.1 Planck had studied another phenomena where the wave model didn’t quite add up known as blackbody radiation. In his work Planck proposed that atoms could only emit light energy in packets. The amount of energy in each packet increases at shorter wavelengths. Einstein proposed that light itself was composed of these packets, or photons, where the energy of each photon is a product of its frequency and Planck’s constant. This means that at higher frequencies photons have more energy, and at lower frequencies they have less energy. In other words, unlike a wave, which can give some or all of its energy to an object, photons can only give all their energy or none of it. So an electron in the metal can either absorb all the energy of a photon (allowing it to escape the metal) or none of it.

This idea explained why higher frequency light caused the released electrons to have more energy, since higher frequency photons give more energy to the electrons. Likewise it explained why brighter light released more electrons. Since brighter light contains more photons, more electrons can absorb a photon to escape the metal. It also explained why bright red light caused no electrons to escape. There is a minimum amount of energy required for the electron to escape the metal, known as the work function. To use our ping pong ball analogy, it takes a certain amount of energy to move the ball off the beach and into the water. Since the photons of red light have less energy than the work function, they can’t give the electrons enough energy to escape. Brighter red light, with more low-energy photons, still leaves the electrons trapped.

Einstein’s solution of the photoelectric effect was one of the foundational works of quantum theory. It opened our eyes to the dual nature of matter, and paved the way to our modern understanding of the cosmos.

Tomorrow: Einstein attacks our intuitive understanding of space and time, and lays the groundwork for his famous theory of gravity.

  1. Einstein, Albert. “Über einem die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt.” Annalen der physik 4 (1905). ↩︎