Khan Academy's Photoelectric Effect Video Lesson

A lot of people use Khan Academy's video lessons. I know that they are quite popular, and I often time get asked about some of the material in the video, both by my students and also in online discussions. Generally, I have no problems with their videos, but I often wonder who exactly design the content of the videos, because I often find subtle issues and problems. It is not unusual for me to find that they were inaccurate in some things, and these are usually not the type of errors that say, an expert in such subjects would make.

I was asked about this photoelectric effect lesson by someone about a month ago. I've seen it before but never paid much attention to it till now. And now I think I should have looked at it closer, because there are a couple of misleading and inaccurate information about this.

Here is the video:



First, let's tackled the title here, because it is perpetuating a misconception.

Photoelectric effect | Electronic structure of atoms

First of all, the photoelectric effect doesn't have anything to do with "structure of atoms". It has, however, something to do with the structure of the solid metal! The work function, for example, is not part of an atom's energy level. Rather, it is due to the combination of all the atoms of the metal, forming this BANDS of energy. Such bands do not occur in individual atoms. This is why metals have conduction band and atoms do not.

We need to get people to understand that solid state physics is not identical to atomic/molecular physics. When many atoms get together to form a solid, their behavior as a conglomerate is different than their behavior as individual atoms. For many practical purpose, the atoms lose their individuality and instead, form a collective property. This is the most important message that you can learn from this.

And now, the content of the video. I guess the video is trying to tackle a very narrow topic on how to use Einstein's equation, but they are very sloppy on the language that they use. First of all, if you don't know anything else, from the video, you'd get the impression that a photon is an ordinary type of "particle", much like an electron. The illustration of a photon reinforced this erroneous picture. So let's be clear here. A "photon" is not a typical "particle" that we think of. It isn't defined by its "size" or shape. Rather, it is an entity that carries a specific amount of energy and momentum (and angular momentum). That's almost all that we can say without getting into further complications of QED.

But the most serious inaccuracy in the video is when it tackled the energy needed to liberate an electron from the metal. This energy was labelled as E_0. This was then equate to the work function of the metal.

E_0 is equal to the work function of the metal ONLY for the most energetic photoelectrons. It is not the work function for all the other photoelectrons. Photoelectrons are emitted with a range of energies. This is because they came from conduction electrons that are at the Fermi energy or below it. If they came from the Fermi energy, then they only have to overcome the work function. These will correspond to the most energetic photoelectrons. However, if they come from below the Fermi energy, then they have to overcome not only the work function, but also the binding energy. So the kinetic energy of these photoelectrons are not as high as the most energetic ones. So their "E_0" is NOT equal to the work function.

This is why when we have students do the photoelectric effect experiments in General Physics courses, we ask them to find the stopping potential, which is the potential that will stop the most energetic photoelectrons from reaching the anode. Only the info given by these most energetic photoelectrons will give you directly the work function.

Certainly, I don't think that this will affect the viewers ability to use the Einstein equation, which was probably the main purpose of the video. But there is an opportunity here to not mislead the viewers and make the video tighter and more accurate. It also might save many of us from having to explain to other people when they tried to go into this deeper (especially students of physics). For a video that is viewed by such a wide audience, this is not the type of inaccuracies that I expect for them to have missed.

Zz.