Accepting a Compliment

11 July 2013

The photoelectric effect Brian Koberlein
The photoelectric effect

If you shine ultraviolet light on a negatively charged metal such as zinc, it will begin to release electrons. This is known as the photoelectric effect, and it has some unusual properties. For example, if you change the frequency (color) of the light, then the energy of the released electrons will change. At higher frequencies the electrons have more energy, and at lower frequencies less energy. On the other hand, if you keep the frequency of light the same and vary the brightness, then the number of electrons released will vary. Brighter light causes more electrons to be released, while dimmer light releases less electrons.

When the photoelectric effect was discovered in the 1800s it was deeply troubling because it defied explanation. It was clear that the light was not creating electrons, it was simply knocking them free of the metal. But since light is a wave the behavior of the released electrons made no sense.

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 experimentally it depends on the frequency.
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.

It was Albert Einstein who found the solution, based upon the energy packet idea of Max Planck. Einstein demonstrated that light was made of particles known as photons. 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. Planck proposed a similar idea with his energy packet concept, but Einstein took it further to say that light was always quantized. 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.

The result is summarized in the equation below. Here K is the energy of the escaping electron, nu (the v) is the frequency of the photon, h is Planck’s constant, and phi (the o with a line through it) is the work function. Einstein proved that light was quantized, for which he won the Nobel prize.

We’ve finally reached a point where we begin to understand the workings of atoms and light and the interactions between them. It is not a world envisioned by Newton and Maxwell, but a world of quanta ruled by Planck’s constant. But what we’ve found seems to hide a deep contradiction. The photons of light stem from the requirement that electrons in an atom act as matter waves. Yet the photoelectric effect proves that light is made of particles because electrons (as particles) are released from the metal.

We therefore have experiments that show light is a wave, and other experiments that show light is made of particles. Likewise we have experiments that show electrons are particles, and others that show that electrons are waves. It should be stressed that all of these experiments are valid and repeatable. Over and over again light is shown to be a particle in one type of experiment and a wave in another. Electrons are shown to be waves in one type of experiment and particles in another.

This seems to be a contradiction, but it is verified by experimental observation. And there is something subtle going on as well. For example, photons are particles with an energy dependent on its frequency. In other words it is a particle with a wave property. The electron matter wave has a wavelength that depends upon the electron’s mass. Thus it is a wave with a particle property. This subtle connection between particles and waves leads us to an idea known as the complementarity principle. It seems that at a fundamental level objects have aspects of both waves and particles. They are both, or neither, or something strangely different.

If this still doesn’t make sense, you’re not alone. The idea is very hard to wrap your head around. At this point all we can do is accept the compliment.

Next Time: Light is a wave, except when it’s a particle. Electrons are particles, except when they are waves. Is there some experiment that makes sense of it all? Yes…and no. Quantum theory comes of age tomorrow.