The chemistry of the actinoid elements is not so smooth as that of the lanthanoids. Justify this statement by giving some examples from the oxidation state of these elements.
The chemistry of actinoids is much more complicated than that of the lanthanoids. This complication arises partly due to the occurrence of a wide range of oxidation states in actinoids and partly because their radioactivity creates special problems in their study.
The actinoids generally show a +3 oxidation state, but the elements in the first half of the series frequently exhibit higher oxidation states. For example, the maximum oxidation state increases from +4 in Th to +5, +6 and +7 respectively in Pa, U and Np, but decreases in succeeding elements. This shows a very uneven distribution of oxidation states among the actinoids.
In contrast, the lanthanoids show close similarities with each other and display gradual variation in properties which do not entail change in oxidation state. The lanthanoids predominantly exhibit the +3 oxidation state with only a few exceptions like Cerium which shows +4 state.
The greater range of oxidation states in actinoids is attributed to the fact that the 5f, 6d and 7s levels are of comparable energies. This makes it easier for actinoids to lose different numbers of electrons and exhibit variable oxidation states.
Since the distribution of oxidation states among the actinoids is so uneven and so different for the former and later elements, it is unsatisfactory to review their chemistry in terms of oxidation states, making their chemistry less smooth compared to lanthanoids.
Explanation
This answer addresses the question by comparing actinoids and lanthanoids specifically in terms of oxidation states. The textbook context clearly states that actinoid chemistry is 'much more complicated' due to wide range of oxidation states and radioactivity. The examples of Th (+4), Pa (+5), U (+6), and Np (+7) showing increasing maximum oxidation states in the first half, followed by decrease in later elements, demonstrates the uneven and irregular nature of actinoid chemistry. The comparable energies of 5f, 6d, and 7s orbitals explains why actinoids show greater variability in oxidation states compared to lanthanoids, whose chemistry is more uniform and predictable.