Final answer:
The opioid medication with a long half-life, suitable for postoperative pain and used at the end of surgical procedures or in the recovery unit, is Morphine. It provides sustained pain control and can act as an analgesic without loss of consciousness.
Step-by-step explanation:
The opioid medication that is appropriate for use at the end of a surgical procedure or in the recovery unit for postoperative pain because of its long half-life is Morphine. Morphine is often used before and after surgical procedures to alleviate severe pain and has the properties of an analgesic, which means it reduces pain without loss of consciousness, as well as being a narcotic in higher doses, reducing pain with drowsiness and loss of consciousness. Unlike medications such as Remifentanil or Alfentanil which have a short duration of action and are used for immediate, short-term pain relief during surgeries, Morphine provides sustained pain control, making it better suited for ongoing pain management post-surgery.