Question

the half-life of iodine-131 is 8 days. how many milligrams of iodine-131 remain after 24 days if the original amount was 4.00 mg?

a. 0.500 mg

b. 0.444 mg

c. 1.33 mg

d. 0.667 mg

Explanation:

Step1: Find number of half - lives

The formula for the number of half - lives \(n\) is \(n=\frac{t}{t_{1/2}}\), where \(t\) is the total time and \(t_{1/2}\) is the half - life. Given \(t = 24\) days and \(t_{1/2}=8\) days.
\(n=\frac{24}{8}=3\)

Step2: Use the radioactive decay formula

The formula for the remaining amount of a radioactive substance is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount, \(n\) is the number of half - lives. Here, \(N_0 = 4.00\) mg and \(n = 3\).
\(N=4.00\times(\frac{1}{2})^3\)
\(N = 4.00\times\frac{1}{8}\)
\(N = 0.500\) mg

Answer:

A. 0.500 mg