To determine whether the bacterium is a chemotroph, the most appropriate method would be:
growing the bacterium in an agar tube filled with protein to see if it breaks the organic molecules down.
Chemotrophs obtain energy by oxidizing chemical compounds (either organic or inorganic). Testing the bacterium's ability to break down organic molecules (like proteins) would help identify if it is a chemotroph. The other methods focus on photosynthesis or carbon fixation, which are more relevant for differentiating autotrophs (like phototrophs) rather than identifying chemotrophs.