Final answer:
It will take 15.0 days for only 1/8th of the original amount of a sample with a half-life of 5.0 days to remain, as it takes three half-life intervals for the amount to reduce to 1/8th.
Step-by-step explanation:
To determine the time required for only 1/8th of the original sample of an element with a half-life of 5.0 days to remain, we need to understand the concept of half-life in the context of radioactive decay. After each half-life interval, half of the remaining sample decays, so after one half-life there is 1/2 remaining, after two half-lives, 1/4 remains, and after three half-lives, 1/8 remains.
Since the half-life is 5.0 days, it will take:
5.0 days for the amount to reduce to 1/2 of the original,
10.0 days for the amount to reduce to 1/4 (which is 1/2 of 1/2), and
15.0 days for the amount to reduce to 1/8 (which is 1/2 of 1/4).
Therefore, it will take 15.0 days for 1/8th of the original amount of the sample to remain.