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What is the photoelectric effect? Why can't multiple low-frequency photons free an electron?

It is known that an electron from a metal will escape if it gains enough energy from a high energy (frequency) photon. Why can't the electron gain more and more energy from several lower energy photons (lower than its work function) and finally escape?

Einstein's simple explanation of the photoelectric effect earned him a Nobel Prize and helped to start the revolution in physics that brought us the modern quantum theory. It's so simple, in fact, that I can explain it in a paragraph. It goes like this: imagine that every beam of light is made up of particles, which we'll call photons. Imagine also that the color (frequency) of the beam of light corresponds to the energy of each photon, and the brightness of the beam corresponds to the number of photons. Now shine the light on a piece of metal. Trapped in the metal are many electrons, each of which requires a certain amount of energy to be freed. Because the energy of each photon in the beam is determined by the frequency of the beam, this means that there is a threshold frequency below which no electrons will be emitted when light shines on the metal. And that's what really happens in experiments. (Just imagine--if you'd thought that up in 1900, you'd have a Nobel Prize yourself. Well, maybe...)

You ask a good question about this scenario. Let's shine a beam of light on the metal such that the frequency of the light is too low for electrons to be emitted, according to the theory above. What if, you say, two of these photons hit the electron, and the sum of their energies is enough to free the electron? Wouldn't we have electrons emitted, no matter how low the frequency?

It is possible, but usually happens seldom enough that it can be ignored unless the intensity of the beam is extremely high. The reason is that when a photon without enough energy to free the electron strikes it, the photon doesn't stick around--it's re-emitted in a time period that's typically very short. That means that a second photon has to strike very soon, while the electron still has the energy from the first photon.

June 2005, Sara Slater (more by Sara Slater) (Like this Answer)

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