Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being:

Lesser energy difference between 5f and 6d than between 4f and 5d orbitals

The answer is (2) Lesser energy difference between 5f and 6d than between 4f and 5d orbitals.

The lanthanides have a large energy gap between the 4f and 5d orbitals, so it is difficult for them to lose electrons from both orbitals. This limits the number of oxidation states that they can exhibit.

The actinides, on the other hand, have a smaller energy gap between the 5f and 6d orbitals. This means that they can lose electrons from both orbitals, which gives them a wider range of oxidation states.

So the main reason why the actinoids exhibit more oxidation states than the lanthanoids is because of the lesser energy difference between the 5f and 6d orbitals.

The other options are incorrect.

(1) 4f-orbitals are more diffused than the 5f-orbitals:  This is not the main reason why actinoids exhibit more oxidation states. The energy difference between the orbitals is more important.

(3) More energy difference between 5f and 6d than between 4f and 5d orbitals:  This would mean that the actinoids would exhibit fewer oxidation states, not more.

(4) More reactive nature of the actinoids than the lanthanoids:  This is a factor that contributes to the larger number of oxidation states in the actinoids, but it is not the main reason.