Final answer:
After 165 years with a half-life of 55 years, approximately 12.5 grams of a 100-gram sample would be left.
Step-by-step explanation:
To determine how much of a 100-gram sample would be left after 165 years with a half-life of 55 years, we need to divide the elapsed time by the half-life to find the number of half-lives that have passed. Given that the half-life of an isotope is 55 years, to determine how much of a 100-gram sample would be left after 165 years, we perform calculations based on the half-life formula. Since 165 years is three times 55 years, we need to halve the original sample three time.
In this case, 165 years divided by 55 years equals 3 half-lives. Each half-life reduces the amount by half, so after 3 half-lives, you would have 100 grams divided by 2, then divided by 2 again, and finally divided by 2 one more time. Using the formula A = A0 * (1/2)n, where A is the final amount, A0 is the initial amount, and n is the number of half-lives, we can calculate that after 165 years, there would be approximately 12.5 grams left of the original 100-gram sample.