Step 1: Understanding the Concept:
Oxidation states of an element depend on how many electrons can be used for bonding. In transition and inner transition elements, electrons from nearby sub-shells can take part if the energy gap between those sub-shells is small.
Step 2: Apply to actinoids:
In actinoids, the \(5f\), \(6d\) and \(7s\) sub-shells have comparable energies. So electrons from all three can be used for bonding. That gives a wide range of oxidation states, from +3 up to +7 (for example in Np and Pu).
Step 3: Check the options:
(A) Actinoid contraction explains the gradual fall in size, not oxidation states. (B) Radioactivity affects stability of nuclei, not oxidation states. (D) \(4f\) and \(5d\) energies being close applies to lanthanoids. So (C) is correct.
Final Answer:
Close energies of 5f, 6d and 7s allow many oxidation states.
\[ \boxed{C:\ 5f,\ 6d\ \text{and}\ 7s\ \text{levels of comparable energy}} \]