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This may be a beginner question, but I keep reading about the wave versus particle view of light and something keeps bothering me. In particular I'm reading about the photoelectric effect and the support it gave to the corpuscular theory of light. In one source it says,

"Suppose light is actually a stream of particles (photons) with the energy of each particle determined by its frequency."

What exactly does it mean for a particle, here, to have a frequency?

M. Enns
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Ryan
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2 Answers2

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The key to understanding how a particle can have frequency is in one key phrase: "Suppose light is actually a stream of particles." When understanding wave/particle duality, it's important to remember that light is neither a wave nor a particle. It is a thing which, in some circumstances can be well modeled as a wave, and in other circumstances it can be well modeled as a particle. In other circumstances, such as those that form in the single-photon double slit experiment, neither model is well suited for describing what occurs, and we instead rely on a more complete quantum model of light. But, in most cases, light behaves similarly enough to either a wave or a particle that we use one of those two simpler models!

In this case, we start off by assuming that light is well modeled as a stream of particles. What are the properties of these particles? In particular, can we find some properties which correspond to properties in the wave model of light. The answer turns out to be "yes, we can."

The frequency of a photon is something that can be computed from its energy, using the formula $E=hf$, where h is plank's constant. Why do we do this? Its because if we have a stream of photons, such that each photon has an energy $E$, and we then look at that light using the wave model instead of the particle model, we see that we have a light wave of frequency $f$. And, of course, the other direction works as well. If we have a light wave of frequency $f$, and we try to look at that same light using a particle model, the energy of each photon will be $hf$.

There are a lot of times where it is convenient to be able to switch back and forth between the wave and particle models of light. Permitting the idea that a particle might have a frequency (defined by $E=hf$) paves the way for rapidly switching back and forth to whichever model is most convenient for the particular circumstances you are exploring.

Cort Ammon
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  • So, I'm asking this question from the perspective of pre QM. I'm aware that light behaves in both ways, but at the time of the discovery of the photoelectric effect, scientists were arguing over whether was a wave OR a particle. So, at that time what would it have meant for a particle to have a frequency? – Ryan Mar 31 '17 at 00:43
  • But perhaps the author just is relating the two views like you suggest. – Ryan Mar 31 '17 at 00:56
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    In that case, simply remove the one sentence that references QM. What it means for a particle to have a frequency is just that:the behavior of the particle is such that it has a state variable which is so closely related to frequency in the wave model that we just call it "frequency." It also has a "wavelength," which is the state variable which the "light is a photon" crowd needed to use to explain how photons could refract and defract. – Cort Ammon Mar 31 '17 at 16:28
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    Remember, science is a descriptive discipline. It describes how things behave, not why they do it. Photons have a frequency because it was a powerful tool to describe the behaviors of light when it was viewed as a particle. They could have used other tools to describe it, but this proved most convenient (partially because of its association with the wave model) – Cort Ammon Mar 31 '17 at 16:30
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You're actually questioning the very fundamental of the nature. I've been studying the quantum mechanics from the undergraduate to the graduate, but I'm still not convinced yet about how the particle picture and the wave picture are exactly correlated. What I do know is that a collection of many light particle called the photon makes macroscopic picture of the wave.

If you're not digging into the quantum field theory (that's what I rarely know), then the following statement would be enough for you: If you want to describe the macroscopic behavior of the light wave, the Maxwell equations will be enough. If you want to know the absorption of the light by the particle or whatever material which has some discrete energy levels, you have to get the particle picture, a "photon", which has the energy of $\hbar \omega$. The total wave energy is nothing but a sum of all energies of the photons in the wave. Then you can easily understand the photoelectric effect.

Donggyu Jang
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