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Copper have $[Ar] 3d^{10} 4s^1$ electron configuration. And Zinc have $[Ar] 3d^{10} 4s^2$ electron configuration.

My question is, what is the right quantum numbers of last electron of copper? Is it $$a. n=3,l=2,m=+1,s=-1/2$$ or $$b. n=3,l=2,m=+2,s=-1/2$$

If I use A, the electron configuration of copper is $[Ar] 3d^{9} 4s^2$ and it isn't stable. But if I use B quantum numbers, it is the same with the last electron of zinc.

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The correct quantum numbers for last electron of Copper ($\ce{Cu}$) would be $B. n=3,l=2,m=+2,s=-1/2$.

if I use B quantum numbers, it is the same with the last electron of zinc.

Yes, last electrons of Both can have same quantum numbers because Pauli Exclusion law says that no two electrons in an atom can have all four quantum numbers same but it doesn't say that two electrons of different atoms can't have all four quantum number same.

Refer this for more.

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