What forms the basis of the malleability and ductility of a metal?

Malleability and ductility in metals are largely attributed to the ability of metal atoms to arrange themselves in layers that can slide past one another without breaking the metallic bonds that hold them together. This characteristic arises from the nature of metallic bonding, where positive metal ions are surrounded by a ‘sea’ of delocalized electrons. As forces are applied to a metal, these layers can shift or slide over each other, allowing the metal to be shaped into thin sheets or drawn into wires without fracturing.

The other options do not adequately account for the key feature of metallic structures that enables malleability and ductility. Covalent bonds are typically found in nonmetallic substances and would not allow for the same kind of movement between layers as metallic bonds do. Strong ionic bonds, while robust, form rigid structures that cannot deform easily, thus limiting malleability and ductility. The compactness of atoms in metals contributes to their density and overall structure but does not explain the sliding ability of layers which leads to malleability and ductility.