Photoelectric effect vs Spectral lines
I think I understand your position now

hat last email did the trick. I now believe I understand what you are talking about. I was thinking in terms of a single electron in a certain orbit imagining that you intended to say that an individual electron at a characteristic frequency (representing a particular spectral line) could only absorb that frequency ... or ... integral multiples of that frequency.

What you are actually talking about is the "integral multiple" aspect of Bohr orbits, i.e. energy levels like Lyman, Balmer, etc. And ... most importantly ... you are thinking in terms of many electrons in all sorts of allowable orbit frequencies (not a specific one). Here, that the electron may absorb only specific wavelengths is apparently at contradiction with photoelectric experiments which imply (almost explicitly) that any frequency above a certain threshold will be "absorbed" thus knocking the electron out of orbit.

Yet, I believe this is the case apparent contradiction ... wave-particle duality ... a mystery wrapped within an enigma ... never to be explained in terms of simple geometry. Light is a particle or wave depending on the experiment. At least that is what they say.

But that is the crux of my solution.

The "ripple on a pond" is the wave aspect which we detect in astronomy and with our eyes. Such a wave may affect any number of electrons in its path anywhere on the pond (generally localized in planar fashion) but only at the permitted resonant frequencies. A wavelength is 'absorbed' and re-emitted ... thus, scattered ... so that light from a star passing through an interstellar gas cloud is missing spectral lines. By absorbed, I mean not that an electron goes to a higher energy level (from one energy level to the next), but rather that the electron wave's amplitude increases above its present energy level ... something like a washing machine on spin cycle but temporarily off balance.

The particle aspect which is measured in the photoelectric effect is that drop that is emitted upward out of the pond when the stone is thrown (which also, simultaneously, caused the circular ripple expanding toward the edges of the pond. This is the "bullet" aspect of the photon. It carries the lion's share of the energy because it does not diminish in transit as does the outward expanding ripple wave. It simply blows the electron off the atomic nucleus.

When we measure the strength of a radar signal, it diminishes as 1/r. But when we measure the energy of the signal (the ability to do work), it is 1/r2 because we are then measuring the energy of the bullets (not realizing that they exist as a separate but congruent aspect of the electromagnetic phenomenon). I do realize this and therefore propose the original experiment of my first letter.

This wraps up the issue for me for now. If you have no further observations then ... my understanding is much the clearer for our exchange.

Adieu! and Muchos Gratias!

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