What are the exceptions to Madelung's rule?

[Tclack]

I hate memorization, but everywhere I look for the exceptions to Madelung's rule, you must memorize the exceptions. I can't see any patterns, I've tried looking at the standard periodic table and the circular table.

Does anyone have any good insight into the exceptions?

If I DO have to memorize, are there any good mnemonics?

 

[alxm]

Does anyone have any good insight into the exceptions?

The most commonly taught exception, and probably the only one worth knowing of, is the 'rule' that filled and half-filled shells have additional stability. This explains for instance why Copper is s¹d¹⁰ and not s²d⁹, and why Chromium is s¹d⁵ and not s²d⁴.

There are other excpetions that don't fall into those categories. Some are because of special-relativistic effects, which become important as elements get heavier and are for instance part of the reason for the lanthanide contraction.

If I DO have to memorize, are there any good mnemonics?

Not that I know of. But why memorize the configurations? I don't know anyone who has them memorized; it's not very useful knowledge in practice. These shifts are often pretty small, and you rarely come across neutral metal atoms isolated in vacuum. So once you have an oxidized metal atom with some surrounding ligands (the far more common situation), that's going to be a lot more important towards defining what it's actual electronic configuration is. (x-tal field splitting, etc)

It's also important to note that the Madelung rule is merely an empirical generalization. So it does not have much deeper meaning than "This is how it is most of the time". So one response to "Why are there exceptions?" is simply: "Why wouldn't there be?".

 

[bjschaeffer]

I hate memorization, but everywhere I look for the exceptions to Madelung's rule, you must memorize the exceptions. I can't see any patterns, I've tried looking at the standard periodic table and the circular table.

Does anyone have any good insight into the exceptions?

If I DO have to memorize, are there any good mnemonics?

There are no exceptions to Madelung's rule as shown on the following Janet type periodic table. The drawings show the orbitals or, more precisely the spherical harmonics from the Schrödinger solution of the hydrogen atom combined with the Pauli exclusion principle :