Elementary question of binding energy

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The discussion centers on the relationship between the interacting energy (U) between two ions in a crystal and the binding energy (W) for one atom. The initial question asks if U is equal to W, suggesting that the binding energy could simply be the interaction energy. However, some sources indicate that W is actually equal to -1/2 U. This discrepancy arises from the fact that binding energy typically refers to the energy required to separate an atom from the crystal lattice, while U represents the total interaction energy between two ions. The negative sign in the equation W = -1/2 U reflects the convention that binding energy is a measure of stability, indicating energy release when ions are brought together. Clarification on these concepts is essential for understanding the energy dynamics in ionic crystals.
td21
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Hello! I asked this question in Physics section but no one replies so i think it is more a chem question.

When it is given that the interacting energy between 2 ions in a crystal is U, is the binding energy W(for 1 atom) equal to U?
i.e. U=W?

I think it's a reasonable guess;but i also look in some books that "W=-(1/2)U"? Why?and which one is correct? I cannot find anything on the internet, thanks for your help.

My chemistry background is also weak so thanks for your help.
 
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Interaction takes two ions, but you want energy per atom, yes?

Sign is just a matter of convention.
 
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