I have a question on the wave theory predictions for the photoelectric effect. According to the wave theory only the intensity should affect maximum kinetic energy of the ejected electrons. Increasing intensity means increasing the magnitude of electric field vector which increases the force exerted on an electron by the incident beam. Hence the greater KE. Another way to look at it is to say that the greater the intensity the greater the energy per second reaching the plate and the greater the KE.
The frequency of the light should not affect the KE. Classically intensity and energy density of electromagnetic wave do not depend on frequency (am I right?).
The explanation above is frequently given in high school and introductory university books. But is it really correct? I started digging this because some of my students insisted more specific information on the classical predictions. I’ll give another explanation which I found from a bit more advanced text.
The force exerted on an electron can be expressed as F = e(E + v cross B) and in case of linearly polarized light E = E0sinwt and B = B0sinwt. The electron gains energy and starts to oscillate. This takes some time. When energy of the electron is equal or just greater than the work function it is immediately ejected from the metal. So electron does *not* gain significant KE and this leads to low kinetic energies no matter what intensity is used. If intensity is greater the electron is released faster. This prediction contradicts with the former because now greater intensity does not imply greater KE.
Which prediction is consistent with Maxwell’s wave theory?
One more question. How would the oscillation of the electron change if unpolarized light was used? In this case the electric field (and the force) changes direction randomly in the plane perpendicular to the propagation of the light ray. Can the electron gain energy if the light is unpolarized?