Question
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
107.1 days
47.6 days
71.4 days
35.7 days
Answers
Answered by
GPT 3.5
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.
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.