Electrons and wave-particle duality

Jan 2009
Not actually homework help, but at around that level. I hope someone will indulge my lay curiosity (and ignorance).

I was reading some articles on modern physics, purely for amusement and education, and realised I would be best served by writing down what I didn't understand about wave-particle duality. I found that, in fact, my ignorance is greater than I at first thought, and I don't really understand waves.

I would be grateful if someone could clear up the following for me:
How much of the wave is an electron (orbiting a nucleus) on at once? Not how many positions (I am aware it can only be in discrete positions), but how much of the orbit? What I mean is this: The orbit of an electron around a nucleus is a closed wave, but my understanding is that the orbit takes time to complete. So (to use a 2D simplification) is it something like this, where each colour represents the same moment in time:

That is, is simultaneity defined in terms of the frequency of the wave?

(I know my drawing of a wave lacks uniformity. Please forgive my ineptitude with Paint as well as my scientific ignorance).

Thank you for your help,

Jan 2009
To answer my own question somewhat, I now see I had completely the wrong idea about electrons orbiting atoms. If they orbit the nucleus, we don't actually know what the path might look like. We know how likely it is to be in a certain place. In fact, some interpretations of quantum theory say it took all possible paths.

The places the electron can be are described by a mathematical function, that's what the closed (standing) wave is. The electron certainly isn't a bead along a wire. That old picture of the atom was messing up my brain :D

The standing wave describes where the electron can be over time. It is actually a necessity that the function, geometrically represented, takes the form of a standing wave. That is, if the wave were not closed ("the ends didn't meet") it would (metaphorically speaking) "pencil" over itself, as the function reiterated (repeated, "came back around") causing interference, and eventually cancel out.

If anyone wants to give a fuller explanation I certainly wouldn't complain :)


PHF Helper
Feb 2009
Another interesting way to think of this is by considering a ‘charge smear’.

Take some jam on your finger and smear it all over a small sphere.

Try as you may you cannot get an even distribution.

Similarly picture the charge of an electron smeared on a shell around the nucleus.

The probability density multiplied by the charge leads to a concept called charge


A wave has a definite wavelength (λ = h / p) but no fixed position ; it is all over.

A particles position however can be thought of but momentum is not easy to

determine. The wave particle duality thus leads to an uncertainty between position

and momentum. In fact the two are related mathematically by the Fourier transform

and any two quantities related by the F.T have a built in uncertainty they need not

be position and momentum
Apr 2010
Term Papers

An electron bound to the nucleus of an atom is often thought of as orbiting the nucleus in much the same manner that a planet orbits a sun, but this is not a valid visualization.

Term Papers