Which one of the following fixes the atmospheric nitrogen but is not an autotroph ?

The correct option is Rhizobium.

Here is a step-by-step explanation of why this is the correct answer:

1. Understanding the Terms:
- Nitrogen Fixation: This is the process of converting inert atmospheric nitrogen gas ($N_2$) into ammonia (${\mathrm{NH}}_3$) or related nitrogenous compounds, making it usable for plants.
- Autotrophs: These are organisms that can synthesize their own food from simple inorganic substances (like carbon dioxide and water) using light or chemical energy.
- Heterotrophs: These are organisms that cannot synthesize their own food and must rely on organic carbon sources (like plants or other animals) for nutrition.

2. Analyzing the Options:
- Oscillatoria, Anabaena, and Nostoc: These are genera of cyanobacteria (blue-green algae). Cyanobacteria contain chlorophyll-a and carry out oxygenic photosynthesis, making them autotrophic. While they are capable of fixing atmospheric nitrogen, they do not satisfy the condition of being a non-autotroph.
- Rhizobium: This is a genus of Gram-negative soil bacteria. Rhizobium species live in a symbiotic relationship with the roots of leguminous plants, where they fix atmospheric nitrogen inside root nodules. Since they depend on the host plant for organic nutrients (carbohydrates and energy), they are heterotrophic (not autotrophs).

3. Conclusion:
Among the given options, only Rhizobium is a nitrogen-fixing bacterium that is heterotrophic (not an autotroph), making it the correct choice.