Re: [Phys-l] Mass and Energy

[John Denker <jsd@av8n.com>]

Savinainen Antti wrote:

> "The difference, originally quaintly called the "mass defect," is, 
> of course, the "binding energy" that serves to hold the nucleus together. ... So where does the "binding energy" that holds these particles together come from?"
>
> I'm a bit confused here. I have thought that the binding energy 
> is the energy that a system *gives away* when bonds are formed; 
> the bonding could be chemical, nuclear or whatever. The mass of 
> the system decreases because part of the initial rest energy 
> ('the mass defect') is transported to the surroundings or 
> manifests itself as kinetic energy of the products. Isn't this 
> the whole idea behind extracting nuclear power?
>
> So I wouldn't like to talk about the binding energy as if it 
> were present in the system to keep it together. 

I don't quite know what to say about this.  Partially-baked thoughts
include:

a) We should all strive to speak as clearly as possible.

b) However, AFAICT it is virtually impossible to utter a completely
unambiguous sentence about binding energy.  It's like asking about
where the national debt comes from.  You have to answer in terms of
money, but money and debt are opposite concepts, and AFAIK there's
no way in English to talk about the flow of the lack of something.
If you try to be concise, it's ambiguous ... and if you try to spell
it out, it's so convoluted nobody can follow it.

> Should I correct my view?

Of course not.

=====================

The real dilemma is the following:

1) I don't think Hugh or Antti (or anybody on this list) is confused
about the physics of what's going on.

However, I'm not ready to say "don't worry about it" because:

2) It is incredibly common for students to be confused about this.

One common nightmare scenario arises in chemistry class.  Consider a
typical chemical reaction (such as combustion):
 a) The reaction involves breaking chemical bonds.
 b) The reaction liberates energy.
 c) There is energy in the chemical bonds, and it comes out when you
  break the bond, the way egg white and egg yolk come out when you
  break an egg.

Items (a) and (b) are true.  Item (c) is totally, diametrically wrong, but
is a very common student misconception.

It is worth confronting this misconception directly, early and often.


Even the conventional terminology of "ground state" is confusing.  When
we do ordinary chemistry or spectroscopy, it is conventional to take the
molecular "ground state" as the zero-energy reference ... but when talking
about fundamental issues is is conventional and helpful to take the
continuum as the zero-energy reference.

It helps to draw lots of diagrams.

Here is an illustrated analogy that is of limited pedagogical value
because it is confusing ... but at least it makes clear the source
of the confusion.

We can speak of atomic and molecular energy levels are like shelves in
the basement.  A highly-excited energy level is like a high shelf ...
high above the basement floor, that is.  All the shelves are still below
street level.  (Note that I said street level, not ground level, for
reasons to be explained below.)  You have to excite the molecule to a
very, very high shelf (by the usual spectroscopic standards) to get it
up to zero energy (i.e. street level, i.e. the continuum).

Here are some levels for ye olde particle-in-a-box:

         ____________               _____________ street level ≡ continuum
            ^        |             |
            |        |             |
            |        |             |
            Eb       |             |
            |        |~ ~ ~ ~ ~ ~ ~|  second excited state
            |        |             |
            v        |- - - - - - -|  first excited state
                     |             |
                     |. . . . . . .|  lowest state (aka "ground" state)
                     |             |
                     |_____________|  bottom of box



The arrow in the diagram indicates the binding energy of the first excited
state.  The binding energy Eb is conventionally positive for bound states,
and indicates how far the state is below the continuum.

In contrast, when we do ordinary chemistry or spectroscopy, it is conventional
to speak of "the" energy of a state as being the energy relative to the lowest
state of that system, i.e. the "ground" state.  Note the conflict:  this ground
state is far, far below what I call street level.  Also beware that this ground
state does *not* coincide with the overall depth of the box i.e. the depth of
the potential well (assuming the box has finite spatial extent).

Only energy differences matter, so the choice of zero-energy reference is just
a matter of convenience.  Choosing the lowest bound state as the reference
makes sense for spectroscopy, because it means you get to subtract two smallish
numbers (rather than two larger numbers).  Choosing the continuum makes sense
when talking about binding energy of the energy of formation, because the
continuum level of one molecule can be compared with the continuum level of
another.  That is, measuring relative to the continuum is more informative
and more expressive.

In any case:  Binding energy is measured down from above;  spectroscopic
energy levels are measured up from below.  Anybody with a reasonable level
of skill should be able to see things both ways.