Step 1: Understanding lanthanoid oxides.
Lanthanoids, when burnt in oxygen, typically form a stable oxide with the formula Ln\(_2\)O\(_3\). This is a common oxidation state for lanthanoid elements.
Step 2: Analyzing the options.
(A) LnO: Incorrect. This is not the typical oxide formed by lanthanoids.
(B) Ln\(_2\)O\(_3\): Correct. This is the correct formula for the oxide formed when lanthanoids react with oxygen.
(C) Ln\(_2\)O: Incorrect. This is not the stable oxide formed.
(D) LnO\(_2\): Incorrect. This is not the common oxide formed by lanthanoids.
Step 3: Conclusion.
The correct answer is (B) Ln\(_2\)O\(_3\).