Wave-particle duality - a function of population vs individual properties?

Both.

'I think it is safe to say that no one understands quantum mechanics'. Richard Feynman

We need to deal with the “Principle of Indeterminacy.” One reason why no one understands QM is that quanta behave differently depending on whether or not they are observed. An example of this is the “2 Slit Experiment. If we let a stream of quanta pass through a barrier with 2 slits then hit a screen they form an interference pattern of light and dark bands (Absolute proof that what we are looking at are waves.) BUT, when we use the photoelectric effect to detect the quanta hitting the screen, we get discrete packets of energy (Absolute proof that what we are looking at are particles). Then it gets really strange. If we put a detector next to either slit so that we know which slit a given quantum went through, but leave both slits open, the pattern disappears. If we know which slit the quantum went through, we get one behavior (no pattern). If we do not know, we get a different behavior (pattern). We must somehow explain how a particle orders of magnitude smaller than the distance between the slits somehow passes through both slits and interferes with itself.

Quantum Mechanics gets out of this mess by introducing the Uncertainty Principle, Indeterminacy, and the Copenhagen Interpretation of QM. If we do NOT know which slit the particle went through, then the particle is "smeared out in equal parts" and goes through both slits. It turns into a fog. As long as it is a fog, it can pass through both slits. That is: The particle occupies a volume of space with some probability. QM says that so long as the position is not known, the particle occupies the entire volume. If we learn its position, the fog condenses into that location and the particle goes through one slit. What indeterminacy says is: The quantum can be in 2 places at once (both slits).

If you send single photons through the slits you get single impacts on the screen. BUT, if you do not know which slit is open AND both are, then there will be areas where photons are not detected that is the exact locations of the dark areas in the interference pattern. ====> Somehow, single photons "know" where to go such that you get the classical result of the 2-slit Experiment

Put another way. You could calculate where the dark bands should be. Put a detector there. Send single photons (particles) and you will not detect any photons hitting the screen. They all hit where the bright bands should be.

Because of the dual nature that electrons have, frequency varies with energy, but this doesn't necessarily mean the electron itself is "shaking faster." The energy of an electron can be set up this way, where E equals the electron's energy, h equals Planck's Constant, and f equals the electron's frequency.

E = hf (double check to adjust / convert terms if using Joules for energy or Electron Volts)

So with this, you can see that frequency increases as the electron's energy increases. And with increased frequency comes DECREASED wavelength because the two vary indirectly. It helps to either think of an electron as a massive particle or treat it as a wave (sinusoid), but one or the other at a time.

The reason that electrons form diffraction patterns instead of behaving as normal massive particles is because all mass has a wavelength and a frequency (look up equations for DeBroglie Wavelength) but because massive particles have such an INCREDIBLY HIGH frequency, the wave properties and patterns are virtually imperceptible, they are almost non-existent. For something as small as an electron (having some, but virtually zero mass) these patterns are observable and sometimes cause electrons to behave more as waves instead of massive particles.

I hope this helps?? But, if not, you can find more help by looking up the Double-Slit Experiment, and researching diffraction patterns (because electrons in a beam passing through a double slit or a diffraction grating behave as a beam of light would.) There are some helpful equations that go with this.

1 Because particles don't interfere and don't have constructive and destructive interference like waves do.

2 magnitude of vibration is not the same as wavelength. For a photon (particle interaction) E = hf, no amplitude involved. For a wave, energy depends on amplitude AND wavelength and frequency. To measure the energy the wave must hit something, then it is a photon.

The problem with considering it a part of population behavior is that interference patterns appear even when you shoot one particle at a time through your double-slit in the classic experiment, so you're left wondering how a single particle can interfere with itself, or whether time is nothing like the way we think of it.