Re: Magnetons

["David L. Bridges" <dbridge9@IDT.NET>]

Hi Lee,

> Questions:
>
>         1. How can the electron be at rest?  Would this not violate the
> Heisenburg Uncertainty Principle?  If the electron is at rest can it
> still be an electron?

The first answer that may pop into one's mind is that an electron at rest
has totally unknown position, and that a precisely known velocity (Delta v =
0) combined with a totally unknown position (Delta x = infinity) can be
consistent with the uncertainty principle.  There is nothing terribly wrong
with this.

Probably more relevant to the topic at hand, an electron in an s-state
(angular momentum L = 0 h-bar) is in some sense at rest in a way in which an
electron in a p-state (angular momentum = 1 h-bar) is not.  I would be glad
to amplify on this, but I don't know how ... :) except maybe to say that
zero angular momentum "must" mean no orbital motion, which would seem to be
the only motion possible for a bound electron, therefore zero angular
momentum must mean no motion ...  But maybe I should stop talking now.

>         2.  Is it a fair simplification of the magneton to say that this
> a model of an atom put into a magnetic field where all of the electrons
> have a spin of 1/2 or -1/2  the sign being indicative of the being along
> the magnetic field or opposite the magnetic field?

I am not sure I have a firm grip on your question, but my inclination is to
say that a magneton is simply a unit of magnetic dipole moment, like a meter
is a unit of distance or an ampere is a unit of electric current.  There are
a couple different magnetons -- the Bohr magneton and the nuclear
magneton -- of different sizes appropriate to different physical situations
(atomic physics of electrons and nuclear physics of protons and neutrons,
respectively).

>         3.  Is there any relationship of the magneton to the Zeeman
> effect?

Yes, in two ways.

An electron "moving in an orbit" can be thought of as a current loop which
generates the magnetic field of a tiny bar magnet.  The strength of this bar
magnet is L Bohr magnetons, where L is the angular momentum of the orbit.

However, an electron "at rest" can be conceived as being both a point charge
and a point bar magnet with its own north and south poles.  The charge of
the electron is the famous 1.6e-19 Coulombs.  The strength of the electron
as a bar magnet is approximately 2 Bohr magnetons.  The fact that an
electron is a tiny bar magnet is related to the fact that electrons have
spin.  It is simultaneously tempting and wrong to think of an electron as a
small ball of negative electric fluid spinning about an axis.  The fact that
electron spin exists is undeniable, but it seems impossible to reconcile it
with any classical image, such as spinning billiard balls.  Electron spin
then becomes a quantum aspect of nature with no classical analog.

The Zeeman effect is a result of energy changes of electron "orbits" due to
the presence of externally supplied magnetic fields.  When the external
magnetic field causes the energy change by acting on the bar magnet
resulting from the orbital motion of the electron, one has what is known as
the normal Zeeman effect ("normal" because early physicists were able to
make sense of it even though they did not know about electron spin).  When
the external magnetic field causes the energy change by acting on the bar
magnet resulting from the electron's own magnetic north and south poles, the
result is the anomalous Zeeman effect ("anomalous" because the same
physicists, not knowing about electron spin, could not make head or tail of
what was happening in their experiments).

Good questions -- David