Step 1 : Understanding the Question
The question asks to identify the specific enzyme that catalyzes the first and most crucial stage of the $C_3$ cycle (Calvin cycle), which involves the fixation of atmospheric $CO_2$.
Step 2 : Key Formulas and approach
The primary reaction of the Calvin cycle is: $RuBP + CO_2 + H_2O \rightarrow 2 \times 3\text{-}PGA$. The approach is to identify the catalyst that allows the 5-carbon acceptor Ribulose-1,5-bisphosphate to react with carbon dioxide.
Step 3 : Detailed Explanation
Carboxylation Step: This is the first step of the Calvin cycle. Here, inorganic $CO_2$ is fixed into a stable organic intermediate, a process essential for the synthesis of sugars.
The Enzyme (RuBisCO): The enzyme responsible is RuBP carboxylase-oxygenase (C). It is often called RuBisCO. It has a unique dual nature where it can bind both $CO_2$ and $O_2$.
Product Formation: The enzyme catalyzes the reaction between RuBP and $CO_2$ to form an unstable 6-carbon intermediate, which immediately splits into two molecules of 3-phosphoglyceric acid (3-PGA).
Importance: RuBisCO is characterized as the most abundant protein on Earth, highlighting its critical role in supporting life through primary production in the food chain.
Step 4 : Final Answer
The enzyme required for carboxylation in the Calvin cycle is RuBP carboxylase-oxygenase. Hence, the correct choice is (C).