Electron Retracing Orbit
Will an electron, in an orbit with other electrons, ever travel
along the same path twice or will it travel in a chaotic path which will
eventually cross every single point in that orbit without ever travelling
along that identical path?
The flippant answer is "none of the above". It is not incorrect to think
of electrons in atomic or molecular orbitals as planets orbiting the Sun.
Electrons obey quantum mechanics, while planets obey Newtonian (classical)
mechanics [more or less because frequently simplifying assumptions are made
about ignoring the gravitational effects of all the other planets. The two
are very different.
Electrons behave more like waves when confined to stable atomic/molecular
states, but even this picture is incomplete, because the "waves" are not
like throwing pebbles in a pond.
Quantum mechanics only allows us to compute the "probability" that an
electron will be at a point in space, and it really is not a "point" in
the Euclidean sense, because the Heisenberg Uncertainty Principle limits
how accurately we can locate the electron's position and its momentum
(mass x velocity). It even gets less intuitive. The position and motion
probability is governed by a function that depends upon several numbers,
called quantum numbers (n, l, m, s). Pauli showed that no two electrons
could have the same exact set of these quantum numbers, so in a sense,
the avoid one another.
All of this is very counter-intuitive, but so far as we know, one has to
toss your intuition out the window (or at least re-train it) in order to
correctly describe the behavior of atoms and molecules. Rather one has to
let the math take us to the result that is consistent with the experimental
data. And this very counter-intuitive package is the best we have to date,
after a century of development.
If you feel uneasy about all this you are in good company. Einstein never
really bought into quantum mechanics, saying famously, "God Does Not Roll
Dice." And physicist Richard Feynman said words to the effect: Anyone who
tells you that they understand quantum mechanics, does not understand the
It is really tough to toss out our intuition and rely on the "long mathy
equations" but that seems to be our only option at the present time.
As we now know from our understanding of quantum mechanics, an electron
is not a point, but is described by a wave. It is therefore spread over
For example, an electron in the lowest Bohr orbit of a hydrogen atom is
equally likely to be at any point around the orbit and at a range of
radii. So at any instant it has some probability, given by its wave
function, of being any place on any of its possible orbits.
To get a fuller understanding, read any elementary text which talks about
quantum mechanics. Not knowing your grade, its hard to make a specific
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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Update: June 2012