Does a) the Calvin cycle, b) pigment, c) the citric acid cycle, d) electron transport chain and e) oxidative phosphorylation take place in photosynthesis, cellular respiration or both?

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I'm going to break this down by process. First, I'll discuss photosynthesis. In photosynthesis, pigments in the chloroplasts (often times in the leaves) absorb specific wavelengths of light to begin the light-dependent reactions. The light-dependent reactions use the energy from light to perform photophosphorylation (similar to oxidative phosphorylation except it is powered by photons of light instead of electron-carrying molecules) which produces ATP and NADPH. There is an electron transport chain that occurs during photophosphorylation, and it has a similar purpose to the electron transport chain in oxidative phosphorylation because it works to set up an electrochemical gradient. The ATP and NADPH produced during the light dependent reactions power the reactions of the Calvin cycle, which produces food for the plant in the form of glucose.

In cellular respiration, glucose is broken down and the energy is converted into ATP. The process begins with glycolysis which breaks glucose down into pyruvate. The pyruvate is then used in the citric acid cycle which produces carbon dioxide as waste and NADH and FADH2, the electron-carrying molecules. These molecules transfer electrons to the electron transport chain which sets up the electrochemical gradient for ATP synthesis. This process is known as oxidative phosphorylation.

So, the electron transport chain is common to both processes, but of the other items in your question are unique to either photosynthesis or cellular respiration.

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