Transition metals have variable oxidation states due to the comparable energies of their (n-1)d and ns orbitals, allowing for sequential electron loss. Manganese shows the widest range, from +2 to +7, because its 3d⁵4s² configuration provides exceptional stability at multiple steps, especially the half-filled d⁵ state at +2. I teach this with conviction, yet at home, my own calculations for my younger son's college fees feel like a different, more painful oxidation series—each higher "state" seeming just within reach until you actually try to balance the equation. One more attempt at the budget, then.
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