The solid which has the described property is aluminium. Aluminium in solid state does not conduct but in its molten state it conducts.
Aluminium is 13th element in periodic table. Al is an electron deficient metal but it is placed among the non-metals since it does not conduct electricity in its solid state.
The boiling point of a substance is the temperature at which it converts from its solid state to liquid state. Al has a boiling point of 2400 °C. It is because of its solid nature and strong intermolecular fore of attraction.
Some solid will breaks easily when a damping force is applied and this breaking tendency is called brittlessness. Al is brittle in nature and not as hard as pure metals.
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