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Why lanthanum, gadolinium and lutetium show different electronic configurations?

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i. It is observed that lanthanum, gadolinium and lutetium show different electronic configuration because the 5d and 4f-orbitals are nearly of the same energy and the distinction between the two is difficult.

ii. Due to this, some extra stability is achieved when the 4f is half-filled and completely filled so the next electron goes in 5d-orbital instead of 4f-orbital. 5d orbital contains one electron in 5d subshell in case of La, Gd and Lu while it is empty in case of other lanthanoids.

iii. f0 , f7 and f14 configurations have extra stability due to empty, half filled and completely filled f orbitals respectively.

iv. The electronic configuration of 57La, 64Gd and 71Lu in +3 oxidation state are as follows:

La+3 : [Xe] 4f0

Gd+3 : [Xe] 4f7

Lu+3 : [Xe] 4f14.

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