In the case of an electron dropping to a lower orbit (circular orbit
for simplicity's sake) around a proton, the total energy (E) of the
system (atom) remains the same. It has lost potential energy (U) by
moving closer to the positive charge. It has gained an equal amount of
kinetic energy (K) because it's velocity must increase for its new
centrifugal force (mv^2/r) to balance the stronger electrostatic force
(ke^2/r^2). It has to move faster (more kinetic energy) in its tighter
orbit because the attractive force is greater at this reduced distance
(more negative potential energy). Total energy (E = U + K ) remains
constant.
This orbiting electron radiates a changing electric field into the
universe due to the motion of its source (the orbiting electron). This
field, and the changes in it, move out (propagate) out from the
electron in all directions at the speed of light. This is similar to
how the static electric field produced by a stationary electron moves
away at the speed of light. In the case of an isolated atom (as Bohr
postulated) the orbiting electron can lose no energy due to radiating
this changing electric field because there is no other charge in the
universe to absorb energy from this field (convert some of its
potential energy into kinetic energy). If another charge is present,
the electric field exerts a force on it and it's electric field exerts
a force on the orbiting electron and each of them can then gain or
lose energy.
The electron remains in a stable orbit and does not spiral in to the
nucleus, contrary to what many of us were taught in Physics 214
(Tippler). This was the third and last college physics course for EEs.
10-20 years ago I figured out why - lol. Too much of it is wrong like
that electron spiraling into the nucleus story which is a clear
violation of electrodynamics.
In the real universe, the orbiting electron's radiated electric field
(E = kq/r^2) exerts a force on all other charges (q) in the universe
including those of the proton it is orbiting. This force (F = Eq) adds
or subtractss kinetic energy (velocity) to/from all other charges in
the universe. These other charges, in turn, radiate an electric field
that adds to or subtracts from the kinetic energy (velocity) of our
orbiting electron. Assuming an equal distribution of charge in the
universe, this force balances out to a net of zero on a large scale
and our electron does not gain or lose any kinetic energy (on average)
from the universe at large. It remains in a stable orbit so the atom
remains stable.
Up close to the orbiting electron, things are quite different. The
electron "feels" an ever changing central force from the nucleus which
does not exactly balance its constant centrifugal force of orbit. This
is due to the positive and negative charges of the proton (and
probably its quark constituents) constantly moving. Therefore the
"center of charge" of the nucleus is constantly moving. The constantly
changing distance and direction to the center of charge causes the
force felt by the orbiting electron to constantly change in magnitude
and direction.
The total force the orbiting electron feels at any time is the sum of
the varying forces from other charges (positive and negative) in the
universe together with the varying and much stronger force from the
closer charges of its nucleus that it is trying to orbit. This force
is almost constant and balances the centrifugal force of the orbiting
electron.
Occasionally, though, a "rogue wave/pulse" of electric field with
sufficient amplitude (strength) hits the electron. This electric field
(force) is sufficient to either eject the electron from orbit
(ionization) or inject the orbit into the nucleus (de-orbit the
electron into the nucleus) which is called electron capture (a form of
radioactive decay).
This ever changing electric field (force) at the electron's location
is practically impossible to calculate so a statistical treatment is
usually employed to predict how often, on average, such "rogue
wave/pulses" will arrive and either eject the electron from the atom
or inject it into the nucleus.
The same applies to electrons or positrons ejected from the nucleus
(beta decay) which also react to the ever changing electric field
produced by all the charges of a nucleus constantly in motion. This is
why radioactive half-lives refer to bulk matter and the actual
ionization of and individual atom or decay of and individual nucleus
is not practically predictable.
These radiated electric fields circumvent the problem of how one
particle causes "action at a distance" on another particle. According
to classical mechanics, this seemed to require a material or medium to
convey the energy and contain the energy as it was in transit from one
particle to the other. The energy of a sound wave is contained in the
potential energy of the compressed air (like a compressed spring
stores energy) as it moves from source to receiver. Maxwell, Mach, and
others, wanted a medium to contain the electric energy while it was
being transferred between the two charged particles in a vacuum. What
was the "nature" of the kinetic energy (K = .5mv^2) and what contained
it while it was in transit between the particles and thereby belonged
to neither of the particles. As kinetic energy is classically defined
as mass in motion, Maxwell proposed the transit occurred through an
aether medium which was extremely rigid yet extremely rarified. These
two attributes seemed contradictory to him. I find it noteworthy that
Maxwell signed off his "Treatise on Electricity and Magnetism" with
the following statement concerning the propagation of light (an
electromagnetic wave): "The idea of an aether cannot be got rid of."
---------------------------------------------------
Michael J. Strickland Reston, VA
---------------------------------------------------