Final answer:
The organism likely causing the heavy urethral discharge in the 20-year-old male is Neisseria gonorrhoeae, which fits the description of gram-negative diplococci and is oxidase positive.
Step-by-step explanation:
The likely organism causing the urethritis with heavy urethral discharge in this 20-year-old male is Neisseria gonorrhoeae. The culture showing gram-negative diplococci with adjacent sides that are flattened and being oxidase positive indicates a gonococcal infection. Gonorrhea is a common sexually transmitted infection (STI), especially prevalent in sexually active individuals who do not use contraceptives. Considering the patient's history and lab results, Neisseria gonorrhoeae is the correct answer, which is option (a).
Among the other options presented, Chlamydia trachomatis (option b) is the causative agent of chlamydia, which can also cause urethritis but does not match the gram stain result of gram-negative diplococci. Trichomonas vaginalis (option c) is a protozoan and would not be visualized as a bacterium in the culture, and Treponema pallidum (option d) is the causative agent of syphilis, identified by different characteristics than those described in the patient's lab results.