Step 1: Understanding the pigments in red algae.
Red algae are unique in that they contain phycobilins, which are red and blue pigments involved in photosynthesis. These pigments help absorb light energy, which is then used in the process of photosynthesis.
Step 2: Analyzing the options.
(A) xanthophyll: Incorrect, xanthophyll is found in many plants but not specifically in red algae.
(B) carotene: Incorrect, carotene is found in plants but not specifically in red algae.
(C) phycobilins: Correct, phycobilins are the key photosynthetic pigments in red algae.
(D) anthocyanin: Incorrect, anthocyanin is a pigment found in some plants, but it is not involved in the photosynthesis of red algae.
Step 3: Conclusion.
The correct answer is (C) phycobilins, as these are the unique pigments in red algae that are involved in photosynthesis.