Final answer:
Zinc is the transition metal that does not show variable oxidation states, as it only has a stable +2 oxidation state formed by the loss of two 4s electrons.
Step-by-step explanation:
Among transition metals, Zinc is unique as it does not show a variable oxidation state. It has only one oxidation state, which is +2. While other transition metals can lose different numbers of electrons from their d- and s-orbitals, resulting in varying oxidation states, Zinc only loses its two 4s electrons to form stable Zn2+ ions and does not have partially filled d-orbitals to lose further electrons from. This is in contrast to elements like iron, which can have oxidation states of 2+, 3+, and 6+, and manganese which can have a range from 2+ to 7+. Transition metals have a wide range of oxidation states because they can lose electrons in both their s- and d-orbitals compared to alkali metals and alkaline earth metals, which usually lose only s-orbital electrons.