a. To find the gross productivity of the corn, we first need to calculate the amount of energy that is being produced by the corn. We can do this by multiplying the net primary productivity by the conversion factor, which is the number of calories per gram of corn:
Gross productivity = NPP / (1 - respiration loss) * conversion factor
Gross productivity = 150 g/m²/day / (1 - 0.333) * 400 cal/g
Gross productivity = 150 g/m²/day / 0.667 * 400 cal/g
Gross productivity = 89,955 cal/m²/day
b. The efficiency of photosynthesis can be calculated by dividing the net primary productivity by the amount of insolation energy that is available:
Efficiency = NPP / insolation energy
Efficiency = 150 g/m²/day / 645 cal/cm²/day * 1000 cm²/m² * 4 cal/g
Efficiency = 0.146%
Therefore, the efficiency of photosynthesis for the corn is 0.146%.