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This was written in a lecture slide:

Two electrons present in the same d-orbital repel each other more strongly than do two electrons in the same s-orbital.

Why is there a difference in the amount of inter electronic repulsion in each orbital? Does it have to do with the shape of the orbital?

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  • $\begingroup$ I thought 3-body interactions are not solvable. The interplay among 4s and 3d orbitals suggest nuclear attraction plays an important role. What is the basis for the assertion? Which s and which d? $\endgroup$
    – jimchmst
    Apr 14 at 19:16

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It is related to the shape of these orbitals, but importantly, also with spin-orbit coupling. Two electrons in one orbital must have spin directions opposite to one another. There is no spin-orbit coupling in s-orbital, so these electrons repel only because of their charge. The electrons in d-orbital share a common direction of magnetic field to align relative to. Given that their preferred positions relative to the non-spherical shape of d-orbital and each other are near opposite ends along the direction of the magnetic field, their spin magnetic moments being opposite contributes to repulsion.

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There are multiple reasons for the above mentioned phenomenon but mainly due to their shape and size. In detail:

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           -[D-orbitals,Source:Google]

1.Shielding: D-orbitals with double-dumbbell shape occupies larger volume of space then the small spherical s-orbitals. This leads to less shielding in d-orbitals.

2.Exchange energy: According to Pauli's exclusion principle,electrons occupying same orbital must have opposite spin states.This leads to a repulsive interplay called Exchange energy which is high in d-orbital due to its complex orientation.Hence,stronger repulsion between electrons.

3.Electron-electron repulsion: Due to the presence of nodal plane and multiple lobes,electrons are more spreaded which leads to more interaction and so, repulsion.

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