conductivity (both thermal and electrical) in metals depends on its resistance, and resistance comes mostly from the rigidity of the molecular structure (if molecules won't get out of the way of electrons, they slow down, so hard metals have higher resistance than soft metals) … see
http://en.wikipedia.org/wiki/Copper#Physical" 
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This is because the resistivity to electron transport in metals at room temperature mostly originates from scattering of electrons on thermal vibrations of the lattice, which are relatively weak for a soft metal.
the softness is caused by the weakness of the metallic bonds … in copper (and silver and gold), they are
not covalent (because those elements have a complete d-shell and only one s-electron on top, see image at http://en.wikipedia.org/wiki/File:Electron_shell_029_Copper.svg" ) …
Contrary to metals with incomplete d-shells, metallic bonds in copper are lacking a covalent character and are relatively weak. This explains the low hardness and high ductility of single crystals of copper.
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Copper, silver and gold are in group 11 of the periodic table, and they share certain attributes: they have one s-orbital electron on top of a filled d-electron shell and are characterized by high ductility and electrical conductivity. The filled d-shells in these elements do not contribute much to the interatomic interactions, which are dominated by the s-electrons through metallic bonds.