Melt atomization kinetic energy

Lindemann <8> has made an interesting application of the new theory in the determination of the frequency of atomic vibration, r, from the melting-point. He assumes that at the melting-point, T the atoms perform vibrations of such amplitude that they mutually collide, and then transfer kinetic energy like the molecules of a gas. The mean kinetic energy of the atom will then increase by RT when the liquid is unpolymerised and the fusion occurs at constant volume this is the molecular heat of fusion. 

The freezing point (or melting point) of a sample is the temperature at which the liquid phase of the material is in equilibrium with the solid phase. In order to enter into the solid state, the molecules (or ions or atoms) of the sample need to settle into an orderly, crystalline lattice structure. The presence of solute particles interferes with this process by getting in the way. So it is necessary to cool the sample to lower temperatures, thereby lowering the kinetic energy of the molecules even further, before they will settle into the solid phase. 

As a metal such as lead melts, what happens to (a) the average kinetic energy of the atoms, (b) the average distance between the atoms ... 

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