Orbital energy and Electronic Configurations

[gemma786]

Hi
I have questions related to the electronic configurations of elements of d and f-block.
First I want to ask a question about the E.C. of Lanthanium. This element has E.C. [Xe]5d¹6s², but according to Bohr-Bury rule 4f-orbitals should be filled prior to 5d-orbital and then Lanthanium’s E.C. should be [Xe]4f¹6s², isn’t? AND this is also the case with Gadolinium in which one electron is promoted to 5d orbital leaving behind half filled 4f-subshell.
AND when we go through the electronic configurations of Actinoids why we find so many ambiguity in their electronic configurations?
At last, suppose effective nuclear charge increases by same amount for 3d , 4d and 5d orbitals for different atoms then in which of these orbitals does the orbital energy will decrease most?

 

[alxm]

First I want to ask a question about the E.C. of Lanthanium. This element has E.C. [Xe]5d¹6s², but according to Bohr-Bury rule 4f-orbitals should be filled prior to 5d-orbital and then Lanthanium’s E.C. should be [Xe]4f¹6s², isn’t?

The Bohr-Bury scheme says a shell has 2n² electrons. You're thinking of the Madelung rule. But the Madelung rule is not absolute, it's merely an approximation. You don't need to go further down the periodic table than Chromium before you find "violations" of it.

AND this is also the case with Gadolinium in which one electron is promoted to 5d orbital leaving behind half filled 4f-subshell.

Not the same phenomenon for Lanthanum, but the same as for Chromium; filled and half-filled orbitals have additional stability due to the Pauli principle/exchange energy.

AND when we go through the electronic configurations of Actinoids why we find so many ambiguity in their electronic configurations?

Actinides. There's no ambiguity; but there's no reason to assume that there would be any simple regularity. The energetic state of every electron depends on that of every other electron, and an atom like Gadolinium has as many electrons as an organic molecule. It depends on the correlation of the electronic motion, which is notoriously difficult to predict, on the exchange energy, which is purely quantum-mechanical, and for heavy elements you have to take into account the effects of special relativity on the core electrons, and spin-orbit coupling effects, as well as effects from the geometric properties of f-orbitals, which shield the nucleus to a significantly smaller extent than the rest.

Thanks to the fact that the energy gap between sub-shells is often relatively large, we have a general 'rule' that holds rather well, under the circumstances. But there's no reason to assume it should always hold.

At last, suppose effective nuclear charge increases by same amount for 3d , 4d and 5d orbitals for different atoms then in which of these orbitals does the orbital energy will decrease most?

If you neglect exchange and correlation, they would all change by the same relative amount, proportional to Z². But you can't accurately model even the core electrons simply as an effective nuclear charge, much less the valence electrons, precisely because of this. It's of no explanatory value for understanding the subtle effects involved in the deviations from Madelung's rule.

 

[gemma786]

Thankyou very much alxm.
I think I need to do a lot of work on quantum mechanics but the stream opted by me doesn't allows me do so !
But anyways thanks.