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Is lanthanum classified as lanthanoids? If yes, then can somebody explain in detail why La has 6s2 5d1 as its electron configuration and Ce has 6s2 4f1 5d1?

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Yes, Lanthanum is classified as a lanthanide although it does not have any electrons in its f orbital.

La does not obey the general rule of lanthanides ([Xe]4f^n 6s^2), but is included in this group due to its characteristics (particularly trivalency) being in accordance with the rest of the group. Such as its atomic radius & ionisation energies.

Ce is another exception to the rule (as are Ga & Lu). It ought to be [Xe] 4f^2 6s^2, but the effective nuclear charge, which is still relatively small, is not great enough for f-orbital contraction to be sufficient for 2e in the f orbital. Thus the energy required to fill the f orbitals with 2e is still greater than the energy required to fill the d orbitals. That being said, it is equally as difficult to fill the 5d orbitals with both electrons, as the f orbital contraction has lowered the energy required enough such that 1 electron can occupy the f orbitals and the other can occupy the d orbitals.

I understand if this isn't the exact answer you are looking for as many areas of periodicity have discrepancies, but reasons can essentially be derived back to a balance between the stability of the species & the energetics arising from the occupation of the electron in available orbitals.

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