Final answer:
A substance with an initial mass of 800.0g decaying to 100.0g in 15 years indicates it went through three half-lives. Dividing the total decay period by the number of half-lives gives a half-life of 5 years option .a) 5 years
Step-by-step explanation:
To determine the half-life of a substance, we need to evaluate how quickly a material decays exponentially over time until only half of the original amount remains. In the provided student question, an 800.0g sample decays to 100.0g in 15 years. The decay goes through several half-lives during this period. Let's find out how many half-lives are incorporated within those 15 years.
Firstly, we start with 800.0g and reach 400.0g after one half-life. After the second half-life, we would have 200.0g, then 100.0g after the third half-life. From 800.0g to 100.0g, we cross three half-lives.
Since it took 15 years for the sample to reduce to 100.0g through three half-lives, each half-life can be calculated by dividing the total time period by the number of half-lives. So, 15 years ÷ 3 half-lives gives us the length of a single half-life which is 5 years.
The correct answer to the question is that the half-life of the substance is 5 years.