Final answer:
After 6 days, a radioactive substance which has a half-life of 1.5 days and an initial mass of 8000 grams will decay to 500 grams.
Step-by-step explanation:
The radioactive half-life is the time it takes for half of a radioactive substance to decay. Since the question states that the substance decreases by 50% every 1.5 days, this rate is the substance's half-life. To calculate the remaining amount of substance after 6 days, we divide 6 by the half-life of 1.5 days to find that there are four half-lives in 6 days (6/1.5 = 4). Starting with 8000 grams, we halve this amount four times to find the remaining quantity.
- After 1.5 days: 8000 g / 2 = 4000 g
- After 3 days (2 half-lives): 4000 g / 2 = 2000 g
- After 4.5 days (3 half-lives): 2000 g / 2 = 1000 g
- After 6 days (4 half-lives): 1000 g / 2 = 500 g
Therefore, after 6 days, there will be 500 grams of the radioactive substance remaining.