use the following graph to answer questions 32 and 33. radioactive decay curve percentage of parent material…

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%

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%

Answer

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\neq0)), 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%