[rpirrie]

Hello--I teach ad chem at my local high school, and would llike to know if anybody can think of a good analogy for the difference between binding energy and the energy needed for fusion. I am 90% certain I have the topic straight in my head--binding energy is what it would take to separate the nucleons, fusion energy is what it takes to overcome the proton repulsions--but I want to be able to explain it to my students clearly, so they realize there is an "energy budget" involved, and that if binding E > fusion E, you get an energy payoff. Thanks!

[gippgig]

You don't have all of it straight - there is an energy payoff if the binding E is negative (i.e., the product nucleus is more stable than the starting nuclei) regardless of what the fusion barrier (the energy needed to overcome the proton repulsion) is. The fusion barrier determines how much energy (how high a temperature) the nuclei must have for fusion to occur (not counting quantum mechanical tunneling, which I believe plays only a minor role). A good analogy is a well at the top of a hill (which is exactly what the plot of energy vs. nuclei separation looks like). The fusion barrier is the height of the hill you have to climb, starting at the base of the hill, to drop something in the well. If the bottom of the well is lower than the base of the hill the result will be more stable (more energy will be released than it took to raise the object (only; not counting you) to the top) which is the case in fusion of hydrogen while if the bottom of the well is higher than the base of the hill the result will be less stable (no payoff) which is the case when heavy ions are collided to make superheavy elements. The height of the hill has no effect on this since the added energy required to raise the object (only) up a higher hill is exactly balanced by the added energy released when the object falls a longer distance. The height of the hill (fusion barrier) only affects how far you have to climb (how much energy the nuclei need to overcome the electrostatic repulsion) to drop the object in the well (fuse).

[rpirrie]

Thanks--nice analogy. I appreciate the help. I must confess to some foggy thinking--forgot to bring up the issue of nuclear stability.

[manonemission]

Hello--I teach ad chem at my local high school, and would llike to know if anybody can think of a good analogy for the difference between binding energy and the energy needed for fusion. I am 90% certain I have the topic straight in my head--binding energy is what it would take to separate the nucleons, fusion energy is what it takes to overcome the proton repulsions--but I want to be able to explain it to my students clearly, so they realize there is an "energy budget" involved, and that if binding E > fusion E, you get an energy payoff. Thanks!

What about the energy to strip the electrons away?  Shouldn't that be factored into the "energy budget?"

[gippgig]

It's insignificant - eV vs. MeV.

[manonemission]

It's insignificant - eV vs. MeV.

I'll try to remember that next time I'm trying to pound all the electrons out of a piece of iron with a hammer.

[Enthalpy]

True, chemical energy is concentrated, more so than most mechanical energy (except for meteoroids and similar), but less so than nuclear energy.

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In fusion reactions, tunnelling is equally important as thermal energy. Very few D and T nucleus have enough time kT to get close enough: this is improbable. But they're helped a lot by tunnelling, which is improbable as well but reduces even more the unlikeliness of fusion by the sole thermal energy. In fact, fusion uses both with about equal unlikeliness.

Bringing D and T to 5fm (one nucleus diameter) distance would demand 300keV (3e9 K) while tunneling reduces it to 20keV (2e8 K).