Final answer:
After four half-lives, which total 32 days for a substance with an 8-day half-life, only one sixteenth of the original sample would remain.
Step-by-step explanation:
The question involves a concept from nuclear chemistry called Half-life, which is the time required for half of a sample of a radioactive substance to decay. Given that the half-life of the substance in question is 8 days, we can calculate the fraction of the original sample remaining after a certain period of time. For instance, if we start with 100 mg of a radioactive isotope and after 8 days (one half-life), 50 mg of the original sample would remain. Continuing this pattern, after 16 days (two half-lives), 25 mg would remain; this is because we only have half of 50 mg left.
Now, considering 32 days, this timespan consists of four half-lives (32 days divided by 8 days per half-life). After the first half-life, the amount is halved (50%), after the second, it's halved again (25%), after the third (12.5%), and after the fourth (6.25%). So after 32 days, which equals four half-lives, the fraction of the original sample that would remain is one sixteenth (1/16).