The greatest range of oxidation states is actinoids is partly attributed to the fact that the following set of levels have comparable energies.

\(5f, 6d, 7s\)

The correct answer is option 4. \(5f, 6d, 7s\).

Let us dive into the reasons why actinoids can exhibit such a wide range of oxidation states and how the energy levels of certain orbitals play a role in this.

The actinoid series includes elements with atomic numbers from 89 (Actinium) to 103 (Lawrencium). These elements have electrons filling the 5f subshell, with the general electron configuration being \([Rn]5f^{1-14}6d^{0-1}7s^2\).

Role of 5f, 6d, and 7s Orbitals

5f orbitals: These are the primary orbitals being filled in actinoids. They are slightly more shielded by the inner electrons compared to the 4f orbitals in lanthanoids, which means they can participate more easily in bonding.

6d orbitals: These are higher in energy than 5f orbitals but still close enough in energy that electrons can be promoted to or removed from these orbitals. This overlap in energy allows the 6d orbitals to contribute to bonding and oxidation states.

7s orbitals: The outermost s-orbitals are generally involved in bonding, as seen in many other elements. The 7s electrons can be easily lost, contributing to various oxidation states.

The comparable energies of the 5f, 6d, and 7s orbitals mean that electrons can be distributed among these orbitals with relatively little energy input or loss. This allows actinoids to exhibit multiple oxidation states, as different combinations of electrons from the 5f, 6d, and 7s orbitals can be involved in bonding.

For example, Uranium can exhibit oxidation states from +3 to +6, and Neptunium can have oxidation states ranging from +3 to +7.

The wide range of oxidation states in actinoids is significant for their chemical behavior. This variability allows them to form a variety of compounds with different properties, making them versatile in both nature and in applications like nuclear technology.

Other Orbital Comparisons

5d, 6d, 7s and 5d, 6f, 7s: These combinations are less relevant because they involve orbitals that are not primarily involved in the actinoid series. The 5d and 6f orbitals do not play a significant role in the chemistry of actinoids compared to the 5f, 6d, and 7s orbitals.

The ability of actinoids to exhibit a wide range of oxidation states is due to the comparable energies of the \(5f\), \(6d\), and \(7s\) orbitals, which allows for flexible electron configurations and the involvement of these orbitals in bonding.

Thus, the correct answer is option 4: \(5f, 6d, 7s\).