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This is probably silly but for transition metals , I know they need to have an incomplete d sub-shell, I know its usually 3d sub-shell, but do they have an incomplete 4d sub-shell?
OCR A, for example, defines it thus: 5.3.1 (b) the elements Ti–Cu as transition elements i.e. d-block elements that have an ion with an
The IUPAC definition defines a transition metal as "an element whose atom has a partially filled d sub-shell, or which can give rise to cations with an incomplete d sub-shell".
According to OCR A, Sc is not TE, according to IUPAC, Sc is a TE.
In answer to your initial Q, the 4s sub-shell is not part of the requirement to be a TE.