Re: [Phys-L] Energy & Bonds

[John Denker <jsd@av8n.com>]

Yesterday on 11/14/2013 01:59 PM, I wrote:

> 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.

Just now I put up vastly improved versions of those
diagrams.

In particular, they now include a contribution from
the atomic core, which is a kinetic energy contribution
that comes into play when the ions get close together.
Without this term, the spring model has *zero* range
of validity.

With this term, you can see that the spring model is
pretty good in a *small* region near the equilibrium
point : 
  separation = 0.1 local units,
  force = 0
That is to say, the black dashed line conforms to the
blue line over a small range.  There is a lot of
interesting physics that happens in this small range
... but also a lot of physics that happens waaaaay
outside this range.

The scale for "breaking a chemical bond" is outside 
the range of validity of the spring model, out by
orders of magnitude, as you can see in the diagrams.