Question

use the following graph to answer questions 32 and 33. radioactive decay curve percentage of parent material remaining (%) number of half - lives elapsed 32. how many half - lives have elapsed when 25% of the parent nuclide is left? a. 0 b. 1 c. 2 d. 4 33. how much parent nuclide remains after three half - lives have elapsed? a. 0% b. 6.35% c. 12.5% d. 30%

Explanation:

Step1: Understand radioactive - decay concept

The amount of parent material after \(n\) half - lives is given by \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount and \(n\) is the number of half - lives.

Step2: Solve for question 32

We want to find \(n\) when \(N = 0.25N_0\). Substitute into the formula \(0.25N_0=N_0\times(\frac{1}{2})^n\). Divide both sides by \(N_0\) (since \(N_0
eq0\)), we get \(0.25 = (\frac{1}{2})^n\). Since \(0.25=\frac{1}{4}=(\frac{1}{2})^2\), then \(n = 2\).

Step3: Solve for question 33

We want to find the fraction of parent material remaining after \(n = 3\) half - lives. Using the formula \(N = N_0\times(\frac{1}{2})^n\), substitute \(n = 3\), we get \(N = N_0\times(\frac{1}{2})^3=\frac{1}{8}N_0\). As a percentage, \(\frac{1}{8}\times100\%=12.5\%\).

Answer:

1. C. 2
2. C. 12.5%