Final answer:
a. 15 h
The half-life of the plutonium sample is 15 hours, as it decays to 25% of its original mass after two half-life periods which add up to 30 hours.
Step-by-step explanation:
To determine the half-life of a radioactive sample, we use the principle that in each half-life period, half of the remaining substance will decay.
Given that a sample of plutonium decays to 25% of its original mass in 30 hours, it means that two half-life periods have occurred, because the substance has halved and then halved again (from 100% to 50%, then 50% to 25%).
Thus, if we divide the total time by the number of half-lives, we can find the length of a single half-life. In this case, 30 hours ÷ 2 half-life periods = 15 hours.
Therefore, the half-life of the sample is 15 hours.