Question 6.1: The oversimplified photosynthesis reaction Light + 6H2O+ 6CO......
The oversimplified photosynthesis reaction
\mathrm{Light+6H_{2}O+6C O_{2}\to C_{6}H_{12}O_{6}+6O_{2}}
requires 4.66\times10^{-18}\mathbf{J} per elementary reaction. Calculate the energy per mole in kilowatt-hours and the energy per ton of carbon synthesized. At least 36 photons are needed to drive the photosynthesis reaction above (in several elementary reactions). Consider a red photon of energy 2.9\times10^{-19}\mathbf{J}. Calculate the energy of one Einstein of red photons (1 mol). How much energy is contained in the photons?
The energy per mole is 2.8 MJ or 0.78 kWh. This corresponds to 0.13 kWh per atom of carbon. This gives 0.011/g of carbon and 10.8 MWh/t. The energy of 1 Einstein of photons is 175 kJ. For 36 Einsteins of photons we have 6.3 MJ. That would give a good efficiency. Actually the real situation is more complicated. The photons which are usually absorbed have a higher energy. Furthermore there are other losses, such as reflection or respiration, which lower the efficiency to something like 5.5 – 7%. Taking into account actual farming conditions over a year leads to an efficiency of about 1% or less.