Final answer:
To ensure the hospital receives 6 grams of Uranium after 8 hours, considering the 2-hour half-life, they must order 96 grams initially, as the substance will halve in quantity 4 times before delivery.
Step-by-step explanation:
The question revolves around the concept of radioactive decay and the calculation of the initial amount of a radioactive substance needed, given a specific half-life and delivery time. We know that the half-life of Uranium in the question is 2 hours, and the hospital requires 6 grams upon delivery, which will be in 8 hours. To determine the initial amount needed, we apply the concept of half-lives; every 2 hours, the amount of Uranium will halve. Therefore, after 8 hours or four half-lives, the Uranium will have halved 4 times.
Let's calculate: Starting with X grams, after 2 hours (1 half-life), we have X/2, then after 4 hours (2 half-lives) we have X/4, after 6 hours (3 half-lives) X/8, and after 8 hours (4 half-lives) X/16. To meet the 6 grams required, we set up the equation X/16 = 6 grams which gives us X = 96 grams.