Why do transition metals have variable oxidation states?

Answer 1

Well, they have many orbitals of similar energy... so they can use them.

The possible oxidation states have already been shown here.

The d-block transition metals often use #d# and #s# orbitals to bond... such as in #pi# back-bonding shown here...

...and the f-block transition metals often use #f#, #d#, and #s# orbitals to bond...

[This is the uranium complex known as tris(cyclopentadienyl)tert-butylisocyanouranium(III).]
Hence, the large pool of valence orbitals allow a flexible selection of oxidation states.

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Answer 2

Henry Antrim

Transition metals have variable oxidation states because they have incompletely filled d orbitals, which allows them to lose or gain electrons to achieve different oxidation states. The presence of multiple oxidation states is due to the ability of transition metals to readily lose or gain electrons from their d orbitals, facilitating the formation of compounds with different oxidation states.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.