National League for Nursing (NLN) Science Practice Exam

What fraction of a sample of the radioactive isotope I-131 will remain after 24 days?

1. 1⁄4.

2. 1⁄16.

3. 1⁄8.

4. 1⁄2.

The correct answer is: 1⁄8.

To determine the fraction of a radioactive isotope like Iodine-131 (I-131) that remains after a given period, you need to know its half-life. The half-life of I-131 is approximately 8 days, which means that every 8 days, half of the remaining radioactive material will decay. In this scenario, after 24 days, which translates to three half-lives (24 days ÷ 8 days/half-life = 3 half-lives), we can calculate the remaining fraction of I-131 using the formula for radioactive decay: After each half-life, the amount remaining is halved. Therefore: 1. After the first half-life (8 days), 1/2 of the sample remains. 2. After the second half-life (16 days), 1/2 of that remaining sample decays, leaving 1/4. 3. After the third half-life (24 days), 1/2 of the 1/4 remaining decays, resulting in 1/8 of the original sample. This concept underlies why the fraction of the sample of I-131 that remains after 24 days is 1/8. The calculations show a repeated halving process over the three