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Electron configuration dispute

Nickel has two atomic electron configurations, 3d 4s and 3d 4s, which are very close in energy; denotes the complete argon core structure. There is some disagreement on which configuration has the lower energy. Chemistry textbooks quote nickel's electron configuration as 4s 3d, also written 3d 4s. 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 3d 4s energy level, specifically the 3d (F) 4s F, J = 4 level.

However, each of these two configurations splits into several energy levels due to fine structure, and the two sets of energy levels overlap. The average energy of states with 3d 4s is actually lower than the average energy of states with 3d 4s. Therefore, the research literature on atomic calculations quotes the ground state configuration as 3d 4s.