Final answer:
After 6 half-lives, you’d be left with 1.25g of a radioactive material if you started with an 80g sample. The closest answer choice to the correct amount is 5g.
Step-by-step explanation:
The question is asking for the amount of radioactive material that will remain after 6 half-lives, given an initial quantity of 80 grams. A half-life is the period of time after which half of a sample of a radioactive substance has decayed. After one half-life, you would have half of the initial material remaining. After two half-lives, you would have half of that remaining, which is a quarter of the initial amount, and this process continues.
Thus, after one half-life, you would have 40g remaining, after two half-lives, 20g, after three half-lives, 10g, after four half-lives, 5g, after five half-lives, 2.5g, and finally, after six half-lives, you would be left with 1.25g. Based on the given answer choices, however, none of them exactly match the correct calculation (1.25g), so there may be an error in the options provided. To be consistent with the closest available option, the answer that is closest to the finalized amount (1.25g) would be: