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Re: [Phys-L] Energy & Bonds



On 11/13/2013 04:33 PM, Bill Nettles wrote:

Yeah, a spring analogy can be troubling.

Yes, troubling, or at least tricky. Alternatives exist.

Consider, however, that if you are separating items that are tied
together, so you must do positive work (and increase the potential
energy) to move them apart.

Yes.

Electrical forces have infinite range, so the ions are never really
roaming free, there is just more potential energy in the system
because you did work to increase the separation.

On the other hand, at large R, the force is very small,
so the ions behave very nearly as if they were free.
And if there is screening involved, the force is even
smaller.

Note the contrast:
-- The amount of /energy/ we have to put in to move
two previously-bound ions apart approaches a maximum
at large R. Draw the graph of a -1/R potential.
http://www.av8n.com/physics/img48/ion-energy.png
Don't forget the minus sign, and don't forget
that -1/R is not the right answer at small R.
++ Contrast this with the ½ k R^2 potential for a
Hookean spring.
-- The /force/ between the two ions is at a minumum
at large R. Draw a graph of the derivative of -1/R.
http://www.av8n.com/physics/img48/ion-force.png
++ Contrast this with the k R force law for a Hookean
spring.

If they get close to other "attractive" particles, they lose
potential energy by attaching to those new particles (with new
springs?). The energy idea works, and if you want to keep the spring
idea, you have to realize that new springs replace old springs, and
enough work can break springs.

I'm not 100% happy with the idea of "broken springs" or
"new springs". In the real world, if you stretch a
garage-door spring until it breaks, it's a big dangerous
mess, with energetic bits of broken spring flying all
over the place. No such thing happens with separated
ions.

With the inter-atomic pseudo-spring, the force in the
spring gets /less/ at large distance, very unlike any
ordinary mechanical spring. At large R it doesn't
matter whether you break the spring or not; it's not
doing anything anyway.

Similarly, rather than a "new" spring, we can say that
a "different" spring comes into play. In some hyper-
theoretical sense it existed all along, but it was
heretofore not significant. It becomes significant
when the ions get close enough.

At some point, rather than visualizing a funny spring,
it becomes easier to just imagine the potential well.
Imaging pulling a wagon full of bricks up out of a
pit, where the path follows a 1/R profile, such that
it is very steep at first but then bends over and
becomes nearly horizontal at large R. When you are
in the flatlands, far from the pit, you hardly even
care that the pit exists.

This picture isn't perfect either, but it gets
around a couple of the problems with the spring
picture.

Note that for molecules (including macromolecules,
including chunks of solid) /at equilibrium/ near the
bottom of the energy-level diagram, the interatomic
force -- including KE as well as PE -- can be modeled
as a spring /to first order/ for small oscilations.
This is not suprising; almost anything is linear to
first order! For large-amplitude oscillations, this
pseudo-spring becomes exceedingly nonlinear.

On 11/13/2013 04:33 PM, Bill Nettles wrote:

the O=O molecule does NOT contain two O atoms,

Not convinced. See below.

How do we know that it doesn't have two O atoms? Because an O=O
molecule will not react with other atoms in the same way that two
separate O atoms will.

Even if you buy the conclusion, which I don't that
argument doesn't hold water. As we go from O to O2,
the reactivity goes down ... but as we go from O2
to O3, the reactivity goes up. Therefore I am quite
sure that reactivity is not a good indicator of what
is or isn't inside.

deuteron IS NOT does not contain a proton and a neutron

That seems unhelpful. There is a /shell structure/
for the nucleons inside a nucleus, more-or-less analogous
to the shell structure for the atomic electrons.
http://en.wikipedia.org/wiki/Nuclear_shell_model
That wouldn't be happening if there were not reasonably
well-defined protons and nucleons running round inside
the nucleus. Like any model, the nuclear shell model
has its advantages and disadvantages ... but it would
be nuts to dismiss it out of hand.