Knowing that the Chemistry of lanthanoids (Ln) is dominated by its $$+3$$ oxidation state, which of the following statements in incorrect?

The chemistry of lanthanoids is indeed dominated by the $$+3$$ oxidation state, so we must judge each statement for $$\mathrm{Ln^{3+}}$$ compounds.

Case A: “Because of the large size of the $$\mathrm{Ln^{3+}}$$ ions the bonding in its compounds is predominantly ionic in character.”
$$\mathrm{Ln^{3+}}$$ ions possess large radii (≈ $$1.06\,$$\r{A} for La$$^{3+}$$ to $$0.85\,$$\r{A} for Lu$$^{3+}$$). Large, highly electropositive cations form compounds where electrostatic forces dominate, giving mostly ionic lattices. Hence statement A is correct.

Case B: “The ionic sizes of $$\mathrm{Ln^{3+}}$$ decrease in general with increasing atomic number.”
Across the lanthanoid series, ineffective shielding by 4f electrons leads to a steady increase in nuclear charge felt by the outer electrons. This “lanthanoid contraction’’ makes the ionic radius drop almost smoothly from La$$^{3+}$$ to Lu$$^{3+}$$. Therefore statement B is correct.

Case C: “$$\mathrm{Ln^{3+}}$$ compounds are generally colourless.”
Most $$\mathrm{Ln^{3+}}$$ ions possess partially filled 4f subshells (e.g., Ce$$^{3+}$$: 4f$$^{1}$$, Pr$$^{3+}$$: 4f$$^{2}$$, …, Tm$$^{3+}$$: 4f$$^{12}$$). Colours arise from parity-forbidden but vibronically allowed 4f → 4f electronic transitions. Only ions with 4f$$^{0}$$ (La$$^{3+}$$) or 4f$$^{14}$$ (Lu$$^{3+}$$, Yb$$^{2+}$$) are colourless; the majority show characteristic pastel shades (pink, yellow, green, etc.). Hence the generalisation that Ln(III) compounds are colourless is wrong. Statement C is incorrect.

Case D: “$$\mathrm{Ln(OH)_3}$$ are mainly basic in character.”
Large $$\mathrm{Ln^{3+}}$$ ions hold hydroxide ions weakly, enabling $$\mathrm{OH^-}$$ to accept protons readily, so the hydroxides act as bases. Across the series basicity decreases because of lanthanoid contraction (charge density rises), yet they all remain predominantly basic. Statement D is correct.

Only statement C contradicts accepted lanthanoid chemistry.

Option C which is: Ln (III) compounds are generally colourless.