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Re: [Phys-L] Energy & Bonds

No, I'm talking about the attractive particle-particle interaction with a force of magnitude
k |q_1| |q_2| / r^2
where the model is that the two particles are connected together by a spring that exerts less force the more you stretch it. Here,
http://www.phys-l.org/archives/2013/10_2013/msg00143.html
John Clement actually used the expression "rubber bands" rather than springs. Again, I find that, in the elastic region, the more you stretch a rubber band the harder it pulls (even though it gets thinner) and if you stretch it beyond the yield point, it won't return to its original length if you release it, and if you stretch it far enough, it breaks. In the elastic region it acts like a spring. In this thread, the model came up in this message:
http://www.phys-l.org/archives/2013/11_2013/msg00061.html
(and earlier in the message to which this message was a response). That's the context in which my comment
http://www.phys-l.org/archives/2013/11_2013/msg00049.html
was written.

The model has a definite appeal to me but because the force law for the springs/bands in the model is so different from the force law for ordinary springs and rubber bands, it seems like it could do more harm than good in terms of the beginner's conceptual understanding of the attractive particle-particle Coulomb interaction. It seems that it could also set them up for misconceptions of harmonic oscillator models where (to first order) the net force acting a particle really is proportional to the displacement of the particle from its equilibrium position. I'm interested in comments from people on this list who have used the spring or rubber band model of the attractive particle-particle Coulomb interaction in the classroom. If you still use it, why? If you don't, why not? Is there research evidence indicating that it is a good model to use? You can buy a constant force spring. Can you buy one that exerts a force that decreases with stretch and yet still snaps back to its unstretched length upon release?

-------------------------

By the way, I like that one about the charged particle in a uniform spherically symmetric cloud of the opposite kind of charge where, when the particle is a distance r from the center of the cloud, it is attracted to the center by the amount of cloud charge closer to the center than it is where that amount goes like r^3 and since the force for constant amount of charge goes like 1/r^2 we have a force that is directly proportional to r. It's a nice aside, but it's not what I'm asking about.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Bruce
Sherwood
Sent: Thursday, November 14, 2013 1:37 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Energy & Bonds

Depends on what you're referring to as to whether a spring is or isn't a good
model for electric interactions at the atomic level. Note that when you
stretch a wire the wire behaves macroscopically in a spring-like manner, in
that the stretch (strain) is proportional to the applied force (stress). That
means that at the atomic level the distances between adjacent nuclei
lengthen proportional to the applied force, hence the
(electric) forces between neighboring atoms are in fact springlike.
Obviously we're not talking about Coulomb's law here, which refers to two
point charges, we're talking about a complex situation of two neutral objects
containing charged particles interacting with each other.

Another place where this strange representation of electric forces shows up
is in the classical interaction of light with matter, in which the electrons in
atoms are modeled as responding to light as though they were attached to
the atom by a spring (maybe with damping), which sounds very odd indeed. I
remember being very puzzled by this as a student.

Here's a situation that I found instructive. Consider the effect of a field
applied to a hydrogen atom. To first order, the electron cloud is slightly
displaced so that its center is no longer at the location of the proton, and the
hydrogen atom is now an induced dipole. How is the amount of the electron
cloud displacement related to the strength of the applied field?
Make a crude model of the electron cloud as a uniform-density sphere of
charge, with a radius of one Bohr radius, R. Let r represent the displacement
of the proton relative to the center of the electron cloud.
The force that the electron cloud exerts on the proton is due just to that
portion Q of the electron cloud inside the sphere of radius r, where Q =
e(r^3/R^3), so F = ke^2(r^3/R^3)/r^2 = (ke^2/R^3)r, a restoring force
proportional to the displacement r. In equilibrium this force is equal to the
force acting on the proton due to the applied field E, which is F = eE, so
(ke/R^3)r = E, and the displacement of the proton is proportional to the
applied field, which means that you can model the response to an applied
field with a spring-like force.

A footnote to this is that for the polarizability P of the hydrogen atom we
have the dipole moment er = PE = (R^3/k)E, so P = R^3/k, in rough
agreement with experimental measurements. (In cgs units k = 1 and the
polarizability has units of cubic centimeters.)

Bruce
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