The half-life of 131I is 8.021 days. What fraction of a sample of 131I remains after 24.063 days?
1/2
1/4
1/8
1/16
Please help. Thank you
How many half days is that?
24.063/8.021 = 3
(1/2)(1/2)(1/2) = 1/8
By the way, I did that simple calculation rather than going through the exponential decay routine because the suggested answers were such simple fractions that I guessed we would have a simple number of half days.
Thanks
You are welcome :)
To find the fraction of a sample of 131I that remains after 24.063 days, we need to determine how many half-lives occurred during that time period.
The formula to calculate the number of half-lives is:
Number of half-lives = (Time elapsed) / (Half-life)
In this case, the time elapsed is 24.063 days, and the half-life of 131I is 8.021 days.
Number of half-lives = 24.063 / 8.021
Calculating this, we find:
Number of half-lives ≈ 3
So, three half-lives occurred during the 24.063 days.
Now, we know that each half-life reduces the amount of the radioactive substance by half. Therefore, after three half-lives, the fraction of the sample that remains is (1/2) raised to the power of the number of half-lives.
Fraction remaining = (1/2)^(Number of half-lives)
Plugging in the value of the number of half-lives:
Fraction remaining = (1/2)^3
Calculating this expression, we get:
Fraction remaining = 1/8
Therefore, the fraction of a sample of 131I that remains after 24.063 days is 1/8.
So, the correct answer is 1/8.