What is the half-life of a radioactive sample that is 75% decayed after 142.8 days?
107.1 days
47.6 days
71.4 days
35.7 days
In order to find the half-life, we need to determine the time it takes for half of the sample to decay. Since the sample is 75% decayed after 142.8 days, that means only 25% of the sample remains.
Let's calculate the half-life:
Let N be the initial amount of the sample, and N/2 be the remaining amount after one half-life.
N/2 = N * (1/2)^n
where n is the number of half-lives
Given that only 25% of the sample remains (75% decayed):
N/4 = N * (1/2)^n
1/4 = (1/2)^n
Taking the log base 2 of both sides:
log2(1/4) = log2((1/2)^n)
-2 = -n
n = 2
Therefore, after 2 half-lives, only 25% of the sample remains. Since each half-life corresponds to 142.8 days:
Half-life = 2 * 142.8 days = 285.6 days
So, the half-life of the radioactive sample is 285.6 days.