To determine whether the unknown bacterium is a chemotroph, the 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 substances. In this case, if the bacterium can break down inorganic sulfur compounds, it would support the classification of the organism as a chemotroph. The other options either test for photosynthesis, carbon fixation, or the breakdown of organic molecules, which are not relevant for determining if the bacterium is a chemotroph specifically.