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If the chlorophyll molecule (its chromophore) absorbs red and blue light and reflects green light, shouldn't the absorbed blue and red light be emitted back when its excited electrons relax?

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It is glad to say that we can enter to this question due to having of valuable theorem of 1st law of thermodynamics. Energy cannot be destroy but it can convert in to another type of energy.The chlorophyll molecule decide it to, become photo energy to chemical energy.

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while happening the electron transport chain electrons are going through the primary receptors. This is not happening as the electrons traveling on a trip, this is really a complicated procedure.While they are passing through the primary receptors some reactions are happening. So from which should be contribute to have energy for this reactions. By the energy of absorbed blue and red lights. So it turns it to chemical energy. It store as ATP, and NADPH. So there is no more way for emit that light away. This scenario is firm by the following.

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Reference
- The Light Reactions of Photosynthesis. In: Biochemistry. 5th ed.

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