Concept:
This question evaluates knowledge of nitrogenase biochemistry and the laboratory techniques used to quantify its activity.
Step 1: Evaluating the Assertion.
Assertion (A) is correct. During nitrogen fixation, nitrogenase inevitably produces hydrogen ($H_2$) as a byproduct. Many efficient nitrogen-fixing bacteria possess an Uptake Hydrogenase (Hup) system. This enzyme recaptures the produced $H_2$ and recycles the electrons back into the system, increasing the overall energy efficiency of the process.
Step 2: Evaluating the Reason.
Reason (R) is also correct. The Acetylene Reduction Assay (ARA) is the standard method for measuring nitrogenase activity. Nitrogenase is "promiscuous" and will reduce acetylene ($C_2H_2$) into ethylene ($C_2H_4$). Since ethylene is easily measured via gas chromatography, it serves as a proxy for nitrogen-fixing activity.
Step 3: Determining the Relationship.
Both statements are accurate scientific facts. However, the fact that we can measure nitrogenase with acetylene (Reason R) does not explain *how* or *why* bacteria use hydrogenase to recycle hydrogen (Assertion A). Therefore, (R) is not the explanation for (A).