# Atomic physics - lattice energy

Question: Why is ionic lattice energy inversely proportional to the radius of the atom?

Most heterogeneous covalent molecules are polar to some extent. The degree of polarity, or the dipole moment, depends on the difference in electronegativity difference between the two atoms. The larger the dipole moment, the higher the ionic character.

What I know: Electronegativity decreases as you go downward in a group, however, the size increases, usually, as you go downwards in a group. Thus, ionic character will increase upon going downward, but the ionic lattice energy will decrease? This seems contradictory. Is this true? And if it is, why is it so?

• This is really more of a condensed matter physics question than atomic physics. Also I think you might need to be more specific about what kind of crystal lattice energy you are talking about, network covalent crystals or ionic crystals. That said it has the potential to be a good question IMO. Jul 4 '14 at 18:28
• @paisanco Is that better? Jul 4 '14 at 18:32
• I'll upvote, let's see what the community thinks. Jul 4 '14 at 18:33
• @paisanco Okay, I just want an answer to this. The fact just struck me as strange, and my teacher doesn't enjoy answering such questions. Jul 4 '14 at 18:34

It really boils down to the fact that the electrostatic potential energy between positively and negatively charged ions in an ionic crystal is inversely proportional to the separation between the ions.

For instance this inverse proportionality shows up in the Madelung constant.

Of course the Madelung constant is an approximation to the lattice potential energy due to ionic interaction, because it treats the ions as if they were point charges. But the principle still applies with ions of finite radii.

You can to first order think of the ionic radius as a lower bound on the lattice spacing in the crystal. So, because of the inverse proportionality to distance in the potential energy, larger separation would lead to lower lattice energy, in general.