Step 1: Understanding the Concept:
Biological nitrogen fixation is carried out by prokaryotes that utilize the enzyme complex nitrogenase to reduce atmospheric dinitrogen ($\text{N}_2$) to ammonia ($\text{NH}_3$).
These diazotrophs can be aerobic, facultative, or obligate anaerobes.
Step 2: Detailed Explanation:
- Clostridium [C]: A genus of obligate anaerobic, spore-forming bacteria.
Free-living anaerobic species like Clostridium pasteurianum fix nitrogen in waterlogged or deep soil layers where oxygen is completely absent.
- Rhodospirillum [B]: A group of purple non-sulfur, photosynthetic bacteria.
They function as photoheterotrophs under anaerobic conditions in the presence of light, where they actively fix atmospheric nitrogen.
- Azotobacter [A]: A well-known genus of free-living, obligately aerobic nitrogen-fixing bacteria.
They protect their oxygen-sensitive nitrogenase enzyme using high respiratory rates and protective proteins.
- Gloeotheca [D]: A genus of unicellular cyanobacteria that fix nitrogen aerobically during the dark phase of their diurnal cycle.
Therefore, the anaerobic nitrogen-fixing bacteria in this list are Rhodospirillum and Clostridium.
Step 3: Final Answer:
The anaerobic nitrogen-fixing bacteria are Rhodospirillum (B) and Clostridium (C).