physical chemistry - Howcome orbitals become 'core-like' when electrons are removed?

It seems to me that f-orbitals for lanthanide metals are treated as 'core-like' when a certain number of electrons have been removed.

Or, as Radiochemistry puts it,

The 4f binding energy is so great that the remaining 4f-electrons are regarded as "core-like". [Italic and emphasis added]

How is this justified exactly?

Effort

I am aware that

• each electron will be harder to remove as Culonic attraction increases with positive ionic charge,

and probably

• lathanide contraction is a part of the explanation.

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You have to check out some of these other threads:

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Original topic: Predominance of III oxidation state for lanthanides