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In solid form the atoms and molecules are very closely bonded and intermolecular attractive forces are high. When a solid is melted, the distance between the molecules and atoms increases. Molecules move, become more mobile and vibrate more. For this to happen, their internal energy is to be supplied by external heating.

Suppose the strength of the forces among atoms-molecules of the element is high.  it takes more heat and higher temperature to give more energy to the molecules, so that they become fluid. So their melting point is higher.

Same way, molecules need much more energy to separate from each other, and escape into gaseous form. The molecules have higher kinetic energy in gaseous form.  In a liquid, if the chemical bonds and electrical (ionic) attractive forces are high, then that compound requires more energy and higher temperature to break the bonds.

So boiling point will be higher for such compounds.
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High boiling and melting points denotes that more energy is reqiured to break down it in smaller compounds or elements
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