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Cu has an unpaired electron in 4s, but it is diamagnetic. I thought that it has to be paramagnetic. What am I missing?

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You can't derive the existence or magnitude of diamagnetic properties just from unpaired electrons. On the contrary, diamagnetism mostly comes from the complete shells. They behave as electric current loops that orient themselves in a certain way in the external magnetic field.

Copper has lots of these complete shells, so the diamagnetic contribution is large. There's also the opposite contribution from the unpaired electron but it's just one electron and the paramagnetic contributions "scale" with the number of these electrons and one is too few. So the diamagnetic terms win.

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What is missing here ist the relation to physical/chemical status of that "copper". What are You talking about? Copper metal? Copper atoms as vapour? Copper ions I or II in aqueous solution? As a matter of fact, copper atoms are paramagnetic (one unpaired electron is enough despite the number of the paired ones!) BTW, the Herren Stern and Gerlach knew that silver atoms are paramagnetic, guess why!. In bulk copper metal the odd electron is sent into the pool of electrons making the metallic bond, thus the metal is diamagnetic, the same is for Cu+ salts, whreas Cu++ salts are paramagnetic.

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I was talking about metal copper. I asked because if you take, for example, Na, which also has an unpaired electron, or Ag, they are paramagnetic. But Cu (metal Cu) is diamagnetic. That's the reason for my question. Thank you very much for your response. –  neutrino Mar 28 '13 at 23:32
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As Lubos has already told, the magnetic property originates from the extent to which electrons are filled in different orbitals.

If you have a look at the periodic table arrangement of d-block elements, you can see that Copper, Silver and Gold are on the same group due to their similar configuration $(n-1)d^{10}\ ns^1$. I don't know whether gold is diamagnetic (My periodic table shows: no data for Gold's magnetic properties). But from the look of copper and silver, gold should be diamagnetic too. These elements have still got an unpaired electron. So, they are paramagnetic. But it's so negligible that their diamagnetic property is enhanced.

It's probably determined by the magnetic moment $\mu=\sqrt{n(n+1)}\ \text{BM}$ (Bohr Magneton) where $n$ is the number of unpaired electrons. Hence, the more number of unpaired electrons an element has, the more paramagnetic character it has.

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