Question

after two half-lives, how much of the original material has decayed?
25 percent
50 percent
75 percent
100 percent

Explanation:

Step1: Understand the concept of half - life

The half - life is the time required for half of a radioactive substance to decay. Let the initial amount of the material be \(N_0\).

Step2: Calculate the amount remaining after the first half - life

After the first half - life (\(t = T_{1/2}\)), the amount of the material remaining \(N_1=\frac{N_0}{2}\).

Step3: Calculate the amount remaining after the second half - life

After the second half - life (\(t = 2T_{1/2}\)), the amount of the material remaining \(N_2=\frac{N_1}{2}=\frac{N_0}{2^2}=\frac{N_0}{4}\)

Step4: Calculate the amount decayed

The amount decayed \(=N_0 - N_2\). Substitute \(N_2=\frac{N_0}{4}\), we get \(N_0-\frac{N_0}{4}=\frac{3N_0}{4}\). Since \(\frac{3N_0}{4}\) is \(75\%\) of \(N_0\)

Answer:

C. 75 percent