Final answer:
Indigo carmine is the dye administered intravenously to visualize and assess the urinary system for immediate damage.
Step-by-step explanation:
The dye that is administered intravenously and excreted by the kidneys to show immediate damage to the bladder or ureters is indigo carmine (a). It is often used in medical procedures to visualize the urinary system, including the kidneys, ureters, and bladder. When injected, it is quickly excreted by the kidneys, which allows physicians to assess the structure and function of the patient's urinary system. Indigo carmine is a blue dye that is excreted by the kidneys, and its presence in the urine can indicate damage to the bladder or ureters. By administering indigo carmine intravenously, healthcare professionals can quickly assess the condition of the bladder and ureters.