problems with interpretation of photoelectric effect
From TVF 4/23/03
Light can only be absorbed or emitted at the critical resonant frequencies of any substance it encounters. That is the origin of spectral lines. Yet, interpreted too simplistically (as I did in my earlier notes), it would imply that most substances should be transparent to most light because they can only absorb certain frequencies; whereas most substances are actually opaque.
So I refreshed on the Rydberg formula for the frequencies at which substances absorb. (I recommend you do the same.) The resonant frequencies are not integer multiples of one another, but do have a relationship to successive integers. It is simply more complex than the orbital analogy might suggest.
For our purposes, what is important is that substances of a specific composition cannot absorb photons below a certain frequency. There is a predictable initial frequency at which absorption becomes possible. But it is a single frequency, not a range. There is then another specific higher frequency (the next integer value in the formula), then another, and so on, with each successive frequency closer to the previous one, until finally one has the series "break" (corresponding to an integer of infinity in the formula). At frequencies above the "break" frequency, absorption is total. (Actually, a second series begins. But eventually, one does reach a frequency above which absorption is total.)
For many substances, these absorption frequencies occur in the range of visible light. But for most substances, they occur in the infrared or lower frequencies. That is why most substances are opaque. Visible light is in the range where absorption is total.
The data you referenced is pretty sparse near the onset frequency. And the targets may be complex metal alloys containing many elements. The preceding theoretical considerations suggest that electron ejections must correspond with absorption frequencies of the target. For example, if the target is a cloud of hydrogen gas, the experiments that led to the Ryberg formula leave little doubt that only electrons of certain discrete frequencies in the visible range are ejected from the cloud. But once we get above a certain frequency (in the extreme ultraviolet for hydrogen), absorption and ejection always occur.
Obviously, physics today does not have a complete model for why these things happen this way. We have only crude analog models. So a range of possible interpretations is available to you for your own modeling. However, your model should work if the target is hydrogen gas too. And I recommend that you try not to make the mistakes of many early 20th century physicists in ruling out some models prematurely. In particular, light being a pure wave is still very much on the table for interpreting the experiments.