Ba-140 has a half life of 13.0 days. What fraction of a sample of Ba-140 will remain after 39 days?
A. 1/8th
B. 1/16th
C. 1/2th
D. 1/4th
To determine the fraction of a sample of Ba-140 that remains after 39 days, we can use the concept of half-life.
The half-life of Ba-140 is 13.0 days, which means that after every 13.0 days, the sample size is reduced by half.
First, we need to determine how many half-lives have passed in 39 days. We can do this by dividing the elapsed time (39 days) by the half-life (13 days):
39 days ÷ 13 days = 3 half-lives
Since 3 half-lives have passed, the fraction remaining can be calculated by taking (1/2) to the power of the number of half-lives. In this case, we raise (1/2) to the power of 3:
(1/2)^3 = 1/8
Therefore, the fraction of a sample of Ba-140 that remains after 39 days is 1/8.
Hence, the correct answer is A. 1/8th.