why do metallically bonded structures conduct electricity

In order for metals to bond they need to loose electrons to ensure that they have a full outer shell and become positively charged. The positive cations (metal ions) are attracted to the negatively charged electrons via an electrostatic force of attraction. The explanation as to why metallic compounds can conduct electricity is due to the fact the cations loose their electrons and these electrons are known as delocalised electrons and are free to move around the metallic lattice, holding a negative charge and allows the compound to conduct electricity.

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