What are the four sets of quantum numbers for nickel?

The four sets of quantum numbers for nickel (n, l, , ) are (3, 2, 0, -1/2).

To find the quantum numbers of Ni, we need to look at its electron configuration. The atomic number of Ni is 28, so its electronic configuration is:

1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁸ 4s² → [Ar] 3d⁸ 4s²   

The last electron is in the d-shell, so let's find the quantum numbers.

Since the shell of the last electron is 3 (3d⁸), this number 3 corresponds to the quantum number n (n=3).

This quantum number is related to the shape of the orbital and is given by n-1. The types of shapes for the values of l are:  

l = 0 corresponds to the orbital's shape "s"

l = 1 corresponds to the orbital's shape "p"

l = 2 corresponds to the orbital's shape "d"

l = 3 corresponds to the orbital's shape "f "  

The shell of the last electron of Ni is 3 (3d⁸), so l is:

This quantum number varies from -l to +l. For Ni, l = 2, so the possible values of are:

This means that we have 5 orbitals, which can have a maximum of 2 electrons (Pauli exclusion principle). Electron filling in those orbitals goes in order from -2 to +2, so for Ni, the last electron is in the 0 orbital.  

Hence, the value of is 0.          

This number can have two possible values: +1/2 (spin-up) or -1/2 (spin-down). For the filling of the electrons in the orbitals, we start for the positive values (+1/2, spin-up) and then we culminate with the negative ones (-1/2, spin-down), to complete the filling of two electrons per orbital. Hence, for Ni, the value of is -1/2 (spin-down).      

Therefore, the four sets of quantum numbers (n, l, , ) for nickel are (3, 2, 0, -1/2).

You can learn more about quantum numbers here: link

I hope it helps you!                            

The quantum numbers for the last valence electron in nickel are (3, 2, 0, -½).

The electron configuration of nickel is [Ar]4s²3d⁸

The last electron added is a 3d electron, so n = 3 and l = 2.

We construct a table of quantum numbers.

Element n  l   mₗ mₛ  

    Sc      3 2   2 +½  

    Ti       3 2   1 +½  

    V       3 2   0 +½  

    Cr     3 2   -1 +½  

    Mn    3 2  -2 +½  

    Fe     3 2   2  -½  

    Co    3 2    1  -½  

    Ni     3 2   0  -½  

The quantum numbers for the last electron in nickel are (3, 2, 0, -½).