Electron Paths and Kepler's Laws
In the physical structure of atoms; how do the electrons
move about? If they are orbits, would Kepler's Laws of Planetary
motion apply to this movement?
1st, what are Kepler's Laws of Planetary Motion?
From this URL:
Kepler's three laws are:
1. The orbit of every planet is an ellipse with the Sun at one of the two
2. A line joining a planet and the Sun sweeps out equal areas during
equal intervals of time.
3. The square of the orbital period of a planet is directly proportional
to the cube of the semi-major axis of its orbit.
Here is a picture of the polar model of an atom:
Here is a picture of the orbits of the planets:
So the difference between the two pictures is that the planets (except Pluto
which is a little bit off from the other planets) orbit the sun in a plane
while atomic electrons orbit the atomic nucleus in several 3 dimensional
But here is the real problem: electrons can show characteristics of a
discrete particle, like planets, AND electrons can show characteristics of
being a wave, like what you see on ponds. Because of this, we really cannot
tell where the electron is. So this is where the comparison of orbiting
atomic electrons to orbiting planets breaks down.
So no, Kepler's laws do not apply to atomic electrons.
To look more deeply into defining the orbits of atomic electrons, please see
this URL about the Heisenberg Uncertainty Principle:
Because of this dual nature of the electrons, quantum mechanics tells us we
can't speak of the location of an electron, but we can only speak of the
probability of where it is.
Kepler's Laws are true because gravity at the level of stars and planets
is a 1/r^2 (one over the distance-squared) force that is also
proportional to the mass of the object in motion. Without the mass
proportion, the law that relates planet orbits to each other (orbit
radius vs. period) would not be true, but the laws that apply to an
individual orbit could still apply. You would see such a thing with a
very large negative charge orbiting a very large positive charge at a
very large distance.
Within an atom, reality is quite different. Concepts of force and
distance "fall apart". An electron no longer has a specific position
feeling a specific force. It is in a specific state with a specific
energy. The electron does not have a path to follow. The electron's
state is called an orbit out of convenience and tradition. Only a few
states can exist for the electron. The electron can jump between orbits
without warning. If "F=ma" were the guiding relationship at the level
of single particles and single atoms, then two of Kepler's Laws would
apply (orbital shape, area vs. time). Without F=ma holding true,
Kepler's Laws do not apply.
You are right. If electrons were solid little balls zipping around
in set orbits they would follow Kepler's Laws and Newton's as well.
But it can be proved that if electrons spun around in such neat
orbits, all atoms would have collapsed by now. They have not and
this is one of the reasons our present concept of the atom does not
look like a miniature solar system.
R. W. "Bob" Avakian
Oklahoma State Univ. Inst. of Technology
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Update: June 2012