Question

uranium-232 has a half-life of 68.8 years. after 344.0 years, how much uranium-232 will remain from a 100.0-g sample?
○ 1.56 g
○ 3.13 g
○ 5.00 g
○ 20.0 g

Explanation:

Step1: Calculate number of half - lives

The formula for the number of half - lives \(n\) is \(n=\frac{t}{t_{1/2}}\), where \(t\) is the time elapsed and \(t_{1/2}\) is the half - life.
Given \(t = 344.0\) years and \(t_{1/2}=68.8\) years.
\(n=\frac{344.0}{68.8}=5\)

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.
Given \(N_0 = 100.0\) g and \(n = 5\).
\(N=100.0\times(\frac{1}{2})^5\)
\((\frac{1}{2})^5=\frac{1}{32}\)
\(N = 100.0\times\frac{1}{32}=3.125\approx3.13\) g

Answer:

3.13 g