To determine whether the unknown bacterium is a chemotroph, the most appropriate method would be:
growing the bacterium in a sulfur solution to see if it breaks the inorganic molecules down.
Chemotrophs are organisms that obtain energy by oxidizing inorganic or organic molecules. By testing the bacterium in a sulfur solution, you can observe if it can utilize inorganic compounds as an energy source, which is indicative of chemotrophic metabolism. The other options either test for phototrophy (using light as energy) or focus on organic molecules, which would not specifically determine if the bacterium is a chemotroph.