Final answer:
The best indication that morphine has been effective is the client's pain score decreasing by 50%, as it is a direct measure of pain relief.
Step-by-step explanation:
A nurse is assessing a client 1 hour after administering morphine for pain, and the nurse should identify the client's pain score decreasing by 50% as the best indication that the morphine has been effective. While it is normal for morphine to cause drowsiness and even sound sleep, this alone is not the best marker for the effectiveness of the medication in pain control. Other physiological responses such as a decrease in heart rate or blood pressure may accompany pain relief but are indirect measures and could be influenced by other factors. Therefore, the direct measurement of pain reduction, exemplified by a significant decrease in the pain score, is the most reliable indicator of analgesic effectiveness.