Why does symmetrical distribution of electrons in d and f orbital lead to greate stability of these or orbitals in comparison to s orbital? [closed]








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My high school textbook mentions the following as on of the reason for why Cr and Cu have thier 3d orbitals filled completely before their 4s orbital.



> 
> The extra stability of d and f orbital is due to:
> Symmetrical distribution of electron :It is well known that symmetry leads to stability . The completely filled or half - filled subshell have symmetrical distribution of electron in them and are therefore more stable . This effect is more dominant in d and f - orbitals . This means three or six electrons in p - subshell , 5 or 10 electrons in d subshell and 7 or 14 in f - subshell forms a stable arrangement
> 
> 
> 


I don't understand why symmetry should lead to greater stability. So I asked my teacher but I was unsatisfied by the explanation and looked over some books and websites but I couldn't understand why symmetrical distribution of electrons should lead to greater stability.


The completely filled s orbital also has Symmetrical Distribution of electrons(at least According to me ,correct me if am wrong) so why are the d orbitals filled completely before the s orbital?How does symmetry leads to greater stability?




I tried to add this as a comment, but I don't have 50 reputation points so I'm replying here.


I don't think symmetry of half-filled orbitals plays much of a role in the stability, look at the electronic configurations of Nb, Tc, Ru, Pt for example. They too have exceptional electronic configurations where the electron enters d orbital instead of s orbital, but in their cases it is not due to partial or full filling of the d orbital. Also, W (tungsten) has a configuration of d4s2, and not d5s1 as would be expected had symmetry of orbitals been the sole reason for stability.


I can't prove this, but it might be because s orbital being small and spherical in shape has less distribution of electrons, and consequently has greater electron-electron repulsion as compared to the d orbital, which might be resulting in these particular electron configurations with an electron in the d orbital instead of the s orbital to be more energetically favourable by having less e--e- repulsions.


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