# Photoelectric effect: V classically independent of intensity

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1. May 5, 2015

### bcrowell

Staff Emeritus
In the photoelectric effect, we observe that the stopping potential is independent of the intensity of the light. This is readily explained by the photon hypothesis. One often sees the statement that in "the classical theory," the stopping potential should increase with intensity.

What classical theory does this refer to?

If people mean the 1924 Bohr-Kramers-Slater theory, there are several problems: (1) it would be odd to refer to it as "the classical theory," when it is actually a hybrid classical-quantum theory; (2) it seems anachronistic to invoke it when discussing Einstein's 1905 photon hypothesis; and (3) BKS was disproved in 1925 by Bothe.

If they really do mean some specific classical theory, then what theory is it? Classically a system of electrically charged particles can't form stable bulk matter, but let's hand-wave that issue away. I would expect that at any particular temperature, the electrons would have a Maxwellian velocity distribution. There would be some rate of emission from the cathode, which would depend on temperature. A visible light wave impinging on the cathode has a wavelength at least a thousand times greater than the size of an atom, so it can't affect one atom without affecting many others in the area equally. I would expect the effect to be simply a warming of the cathode, and the amount of warming would depend on things like the intensity of the light and the ability of the cathode to get rid of its heat. Under ordinary conditions, this warming would be negligible. In any case, there would be no well-defined stopping voltage. Electrons would come out of the cathode with some continuous velocity distribution shaped like the tail of a Maxwellian distribution.

I would like to avoid having this thread sidetracked by a discussion of the claim by Lamb and Scully that the photoelectric effect can be explained without photons. I think their argument is bogus, for reasons given here: http://physics.stackexchange.com/questions/68147/can-the-photoelectric-effect-be-explained-without-photons . In any case, they're invoking BKS, and BKS seems irrelevant to me for the reasons described above.

Last edited: May 5, 2015
2. May 5, 2015

### ZapperZ

Staff Emeritus
The increase in intensity in this case refers to increasing the amplitude of the wave, which is the classical representation of light. For example, if you increase the amplitude of oscillation of a mass-spring system, you have increased the energy of the system while keeping the frequency constant. The wave picture of light intensity corresponds to the amplitude of the wave, and so increasing it corresponds to increasing the "energy" of the wave and light.

I do not believe increase in intensity was connected to the increase in heating of the cathode.

Zz.

3. May 5, 2015

### bcrowell

Staff Emeritus
I agree.

This is what I'm asking. Is there some classical model that predicts that there is a photoelectric effect, that there is a well-defined stopping potential, and that the stopping potential should increase with intensity? If so, then what is that model?

4. May 5, 2015

### ZapperZ

Staff Emeritus
But I think this was expected when you increase the intensity in the classical wave picture. This is because you increase the intensity, you also increase the energy of the oscillation. So the light impinging the cathode has a higher energy than before. Naturally, you expect that the photoelectrons should also receive more energy and come out with higher KE.

Zz.

5. May 5, 2015

### bcrowell

Staff Emeritus
Yeah, I looked at a couple of books that make this claim, and that does seem to be their reasoning. It's total nonsense, however. They don't really come out and say it, but it seems that they're treating the electrons as if they were sitting there in vacuum and being acted on by a light wave, after which they have some kinetic energy. That's nothing like the actual situation, and I don't believe that any remotely realistic classical model would actually produce the claimed result. So it seems to me that this supposed dependence of the stopping potential on intensity is a totally bogus thing to talk about. You can't make a classical model that obviously leaves out major features of the system, and then say, "Hey, my classical model fails, and therefore classical physics is disproved."

Last edited: May 5, 2015
6. May 5, 2015

### ZapperZ

Staff Emeritus
But the issue here isn't whether the claim is realistic or not. It is whether this is the picture that was understood pre-1900. After all, this topic is often presented with a bit of historical context. If it is, then considering the number of smart people who thought of it this way back then, it is obviously a "realistic" model for them, especially when they knew nothing about what is going on inside the material. All they knew was that increasing the brightness of light increases its energy, and one might reasonably expect that this will cause an increase in the energy of the photoelectrons. More energy in, more energy out.

Zz.

7. May 6, 2015

### bcrowell

Staff Emeritus
I haven't seen any evidence of how physicists thought of it back then. These textbook statements smell to me more like sloppy textbook stuff that only became popular among textbook authors long after the quantum theory had been established. (IIRC Stephen J. Gould wrote a nice essay on the unoriginality of textbook authors, using as an example the widespread presentation of Lamarckian evolution in contrast to Darwinian evolution, with the giraffe's neck as an example.) I'm not saying that you're wrong about the historical understanding of the phenomenon; you could be right, but I just haven't seen any such evidence. A vague textbook statement that "according to the classical theory, one expects ..." is not historical evidence.

I also haven't seen any classical description that I would dignify with the term "model." In particular, I haven't seen any classical description that predicts that for a solid metal cathode, the photoelectric effect exists and there is a finite stopping voltage. Again, I'm not saying that no such classical description exists; I just haven't seen one.

My guess would be that the actual historical situation was something more like the following. The photoelectric effect was a complete Kuhnian anomaly in classical physics. It was unanticipated and discovered purely empirically by Hertz, by accident. The existence of the effect and the list of its observed characteristics were completely beyond the reach of classical physics to model. Therefore there was probably no serious attempt to construct models, and people simply set it aside as an anomaly.

Last edited: May 6, 2015
8. May 6, 2015

### wabbit

Interesting. Einstein in his http://hexagon.physics.wisc.edu/teaching/2015s%20ph531%20quantum%20mechanics/interesting%20papers/einstein%20photoelectric%201905.pdf [Broken] says
Referring to P. Lenard, Ann. Phys., 8, 169, 170 ( 1902).
So the answer might be in that Lenard paper, but I don't have it.

Last edited by a moderator: May 7, 2017
9. May 7, 2015

### bcrowell

Staff Emeritus
Good eye. Einstein appears to be referencing two pages within that paper, which seems to be Ann. Phys. 313, issue 5, pages 149-198 (1902). The title and first sentence are:

Googling on these pops up the text of the paper in google books, with an offer to translate it. However, the translation didn't seem to work in my browser.

10. May 7, 2015

### bcrowell

Staff Emeritus
I worked out how a free electron should respond to a plane electromagnetic wave, and assuming that my calculation is right, it simply oscillates with a constant amplitude. There is a transverse oscillation and a longitudinal one. The velocities of these oscillations go like $(e/\omega m)\sqrt{4\pi kS/c}$ and $(4\pi k/c^2)(e/m\omega)^2S$, where S is the Poynting vector. For UV light with an intensity of 1 W/m2, these velocities are about 10^-4 and 10^-15 m/s, so clearly this isn't going to work as a classical model of the photoelectric effect. There is no mechanism for the energy to accumulate.

Maybe a better possibility for a classical model would be a free electron subject to a damping force.

Last edited: May 7, 2015