Final answer:
Heroin is the semi-synthetic opiate that is more potent than its parent compound, morphine, with only 3 mg needed to match the analgesic effect of 10 mg of morphine.
Step-by-step explanation:
The semi-synthetic opiate that is 2-3 times the analgesic potency of its parent compound, morphine, is heroin. Heroin is derived from morphine through a chemical modification that significantly increases its potency. While morphine is a major pain-relieving drug found in opium and is approximately 10% of the crude exudate, heroin does not occur naturally and is produced to have a stronger effect. In fact, it takes only 3 mg of heroin to produce the same analgesic effect as 10 mg of morphine.
Within the realm of opioids, which also includes morphine, methadone, and codeine, heroin stands out due to its enhanced effectiveness and propensity for addiction. Codeine, on the other hand, is structurally similar to morphine but is much less potent. It should be noted that all opioids carry a risk for abuse due to their impactful analgesic and euphoric properties.