Question

Can elements have multiple quantum numbers? I am writing the quantum number for nickel and so far I have the following:
n = 3
l = 2
ml = 0 (can I choose any number between -2 to +2?)
ms = -1/2 (Can I choose -1/2 or +1/2?)
Is this correct?

Answer 1

The quantum numbers reference to the electrons, each electron in an atom has a different set of four quantum numbers. So each of the 28 electrons in the Ni atom has a different set

Answer 2

http://www.angelo.edu/faculty/kboudrea/general/quantum_numbers/Quantum_Numbers.htm

Answer 3

Electron configuration dispute
The nickel atom has two electron configurations, [Ar] 3d8 4s2 and [Ar] 3d9 4s1, which are very close in energy – the symbol [Ar] refers to the argon-like core structure. There is some disagreement as to which should be considered the lowest energy configuration.[6] Chemistry textbooks quote the electron configuration of nickel as [Ar] 4s2 3d8,[7] or equivalently as [Ar] 3d8 4s2.[8] This configuration agrees with the Madelung energy ordering rule, which predicts that 4s is filled before 3d. It is supported by the experimental fact that the lowest energy state of the nickel atom is a 3d8 4s2 energy level, specifically the 3d8(3F) 4s2 3F, J = 4 level.[9]

However, each of these configurations in fact gives rise to a set of states of different energies.[9] The two sets of energies overlap, and the average energy of states having configuration [Ar] 3d9 4s1 is in fact lower than the average energy of states having configuration [Ar] 3d8 4s2. For this reason, the research literature on atomic calculations quotes the ground state configuration of nickel as [Ar] 3d9 4s1.[6]