Final answer:
The fraction of a radioactive sample left after 15 hours, given a half-life of 5 hours, is 1/8 of the original sample. This result is acquired by halving the sample three times, corresponding to the three half-lives that have passed.
Step-by-step explanation:
The question involves understanding the concept of the half-life of a radioactive substance, which is a key idea in both chemistry and physics. The half-life is the time it takes for half of the original sample to decay. After one half-life, there would be 1/2 of the sample left; after two half-lives, 1/2 of 1/2 would remain (which is 1/4); and after three half-lives, 1/2 of 1/4 would remain (which is 1/8).
Since we are looking at a time span of 15 hours and the half-life is 5 hours, three half-lives would have passed. Therefore, the fraction of the original sample that would be left after 15 hours would be 1/8, which corresponds to option B) 1/8.