I am not sure if my answer will be of any help to you, since you phrased your question very broadly.
Differently colored algae developed independently through evolution (red, brown and green algae). All of them developed a photosynthesis mechanism (again independently from one another). Therefore the mechanisms of converting light to energy are not the same for all algae. They use different wavelengths of light to accomplish the same task. The function of all of them, that is providing energy to the algae, is the same. It's just done differently.I hope this answer helps you and further triggers your interest in science.
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