Synthesis of each molecule of glucose in photosynthesis involves

Photosynthesis takes place in two broad stages: the light reactions and the dark reactions. The energy-rich molecules $$ATP$$ and $$NADPH$$ are first produced during the light reactions. These molecules are then consumed in the dark reactions, also called the Calvin cycle, to build one molecule of glucose $$\left(C_6H_{12}O_6\right).$$

The Calvin cycle can be thought of as occurring in three linked sub-processes:

1. Carboxylation - Each molecule of $$CO_2$$ is attached to a molecule of ribulose-1,5-bisphosphate (abbreviated $$RuBP$$). No $$ATP$$ is used in this step.

2. Reduction - The unstable six-carbon product formed in carboxylation splits into two molecules of 3-phosphoglycerate (3-PGA). Each 3-PGA is then converted to glyceraldehyde-3-phosphate (G3P). For every $$CO_2$$ fixed, this conversion consumes two molecules of $$ATP$$ along with two molecules of $$NADPH$$. Hence, for one molecule of $$CO_2,$$ the $$ATP$$ cost in the reduction phase is:

$$\text{ATP}_{\text{reduction per }CO_2}=2$$

3. Regeneration - Most of the G3P produced is not immediately turned into glucose; instead, it is recycled to regenerate the original $$RuBP$$ acceptor so that the cycle can continue. For each $$CO_2$$ fixed, one additional $$ATP$$ is consumed during regeneration. Therefore,

$$\text{ATP}_{\text{regeneration per }CO_2}=1$$

Putting these observations together, the total $$ATP$$ required for one molecule of $$CO_2$$ entering the Calvin cycle equals the sum of the two contributions just stated:

$$\text{ATP per }CO_2 = 2 + 1 = 3$$

But in order to make one complete molecule of glucose, the plant must incorporate six molecules of $$CO_2$$ because a glucose molecule contains six carbon atoms. Therefore, the overall $$ATP$$ requirement becomes

$$\text{Total ATP for }6\ CO_2 = 6 \times 3 = 18$$

Consequently, synthesizing a single molecule of glucose via the Calvin cycle needs precisely eighteen molecules of $$ATP.$$ None of the other option figures (8, 6, or 10) match this detailed stoichiometric calculation.

Hence, the correct answer is Option C.