Copper has one valence electron and Zinc has two?
Copper can be in three forms Cu (I), Cu (II) and Cu(III) whereas Zn can only become 2+. It is rare for copper to lose 3 electrons, but it is possible. To find out how this occurs, check out terms like multivalent and polyvalent in your chem textbook.
well the fact is the electronic configuration of copper would have been (4s-2),(3d-9)...but what happens is one electron from 4s orbital jumps into the 3d orbital giving more stability and a sate of lesser energy..and the new electronic configuration becomes 4s-1,3d-10..... where as Zn has both 4s and 3d orbitals filled and thus cannot loose it because they provide stability!...now in case of copper if the only electron from 4s is lost then it has 3d orbital filled which is again a stable state! thus that electron is available as free electron..... only thing is that if copper looses that electron then it becomes more stable.. while in zinc the 4s orbital is filled and thus provides extra stability..in short the electron cannot be made freely available for stability reasons......thus copper has more free electron than zinc!