How do carbon atoms move from fossil fuels through photosynthesis and respiration?

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In the carbon-oxygen cycle how does the process of photosynthesis and respiration interconnect?
what pathways does a carbon atom go tom a fossil fuel to becoming a part of air that a person can exhale?
 
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This sort of looks like a homework question.. If it is, you want to post those under homework, coursework, textbook questions. You also need to show us your thoughts, how you would go about answering the questions, then we can steer you in a positive direction. (see https://www.physicsforums.com/showthread.php?t=94388)

If this is not a homework question, I would give you this clue on first question. Think about what substances are needed and generated from each process. For the second question (you probably want to clarify your wording), think of what form carbon takes in a fossil fuel, does it stay that way indefinately? If not, how can it be released and what form will the carbon then have?
 
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you can think of in what state plants take carbon for photosynthesis.
 
look at the calvin cycle, look at the respiratory/phosphorylation pathway and come up with something. there is no brief answer to this.

as for the second part, it is interesting in that the O2 given off by the plant does not come from CO2. likewise, the O2 that we breath in gets reduced to water, the CO2 that we breath out comes from the sugar.

it is also interesting to ask a group of students where the actual matter of a plant (such as a tree, for instance) comes from...most will say nutrients in the soil, but the actual carbon matter that becomes the tree comes from the air around us.