Final answer:
The half-life of Po-218 is 3 minutes. It will take 18 minutes for only 1.0 gram of Po-218 to remain.
Step-by-step explanation:
The half-life of a radioactive isotope is the time it takes for half of the sample to decay. In this case, the half-life of Po-218 is 3 minutes.
To determine how long it will take for 1.0 gram of Po-218 to remain, we can use the concept of half-life. We start with 20.0 grams, and at each half-life, the amount of Po-218 is halved. Therefore, we need to find the number of half-lives it takes for the amount to reduce from 20.0 grams to 1.0 gram.
Each half-life is 3 minutes, so we divide the total time by 3 to find the number of half-lives. If it takes 3 minutes for one half-life, it will take 3 x (number of half-lives) minutes for the amount to reduce to 1.0 gram. So, we have:
20.0 grams / 2 = 10.0 grams (1 half-life)
10.0 grams / 2 = 5.0 grams (2 half-lives)
5.0 grams / 2 = 2.5 grams (3 half-lives)
2.5 grams / 2 = 1.25 grams (4 half-lives)
1.25 grams / 2 = 0.625 grams (5 half-lives)
0.625 grams / 2 = 0.3125 grams (6 half-lives)
So, it will take 6 x 3 = 18 minutes for only 1.0 gram of Po-218 to remain.