Problem #2: Power Plant Photosynthesis converts energy from sunlight into chemic

Question

Problem #2: Power Plant

Photosynthesis converts energy from sunlight into chemical energy. How efficient is this process? Let’s consider photosynthesis at a very basic level. We’ll assume that the basic reaction is:

water + carbon dioxide + energy glucose + oxygen

Metabolizing one mole (6.02×1023 molecules) of glucose releases 2900 kJ. In a plant, producing one molecule of glucose might take an energy input of 50 photons of wavelength 600 nm, ignoring losses due to absorption, reflection, etc. Given these numbers, what is the efficiency of this basic process?

Explanation / Answer

energy of 50 photons of wavelength 600 nm is

E = 50*hc/wavelength

E = 6.6*10^-34*50*3*10^8/600*10^-9

E = 1.65 * 10^-17 J for one molecule

for one mole (6.02×1023 molecules) , energy, E = 1.65 * 10^-17 J*6.02×1023 = 9.9*10^6 J

Efficiency = 2900000/9993300 = 0.29

29 percent efficient

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