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Metallic bonding occurs between copper atoms. Only copper is a metal and has the characteristics needed for metallic bonding.

Metallic bonding occurs between atoms with low electronegativities (low tendency to attract electrons from other atoms) and low ionisation energies (little energy required to remove electrons from the atoms). The low tendency for the metallic atoms to keep their electrons allow their electrons to be shared between the atoms, which thus become cations. The cations tend to be very closely-packed; they are not repulsed by their similar positive charges, but attracted to the electrons flowing freely between the cations.

Metallic bonding therefore occurs between copper atoms, which have low electronegativity and ionisation energy. Chlorine atoms have some of the highest electronegativity and ionisation energy of all elements, and thus do not exhibit metallic bonding.

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Q: Does metallic bonding occur between atoms of copper or chlorine?
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