Final answer:
Technetium-99m has a half-life of 6.01 hours, and a patient can leave the hospital once 75% has decayed. This requires two half-lives, totaling 12.02 hours, after which 75% would have decayed and the patient can safely leave.
Step-by-step explanation:
The question pertains to the radioactive decay of technetium-99m and the time required for it to decrease to a safe level for a patient to leave the hospital. Technetium-99m has a half-life of 6.01 hours. If a patient is safe to leave the hospital once 75% of the dose has decayed, this means they must wait until only 25% of the original dose remains.
To calculate this, we utilize the concept that every half-life reduces the quantity of the substance by half. So after one half-life (6.01 hours), 50% of the technetium-99m would remain. After a second half-life, another 50% of that amount would decay, leaving 25% of the original amount. Consequently, two half-lives must pass for 75% of the compound to decay.
Thus, 2 × 6.01 hours = 12.02 hours must pass before the patient is considered safe to leave the hospital. The correct answer is (c) 12.02 hours after injection.