Autotrophic bacteria are organisms that produce their own food from inorganic substances using an energy source, such as light or chemical reactions. Let's go step by step:
Option A: Aerobic biodegradation of organic matter is typically carried out by heterotrophic bacteria that rely on organic matter for energy. This is not a function of autotrophic bacteria.
Option B: Anaerobic biodegradation of organic matter is also a function of heterotrophic bacteria. Autotrophic bacteria are involved in processes like nitrification, not the breakdown of organic compounds.
Option C: Aerobic nitrification is carried out by autotrophic bacteria, such as Nitrosomonas and Nitrobacter. These bacteria oxidize ammonia to nitrites and then to nitrates using oxygen, which are essential steps in the nitrogen cycle. This is a typical activity of autotrophic bacteria.
Option D: Anaerobic denitrification is carried out by heterotrophic bacteria. This process involves reducing nitrates to nitrogen gas, usually in the absence of oxygen.
Thus, the correct answer is Option (C), as it specifically describes the activity of autotrophic bacteria.