OHST Practice Exam

How many years does it take for a radioisotope with a half-life of one year to reduce its activity to less than 10%?

1. 1 year

2. 2 years

3. 3 years

4. 4 years

The correct answer is: 4 years

To determine how many years it takes for a radioisotope with a half-life of one year to reduce its activity to less than 10%, we can use the concept of half-lives. The half-life is the time required for half of the radioactive substance to decay. Initially, we start with 100% activity. After one half-life (1 year), the activity decreases to 50%. After two half-lives (2 years), the activity decreases to 25% (which is still greater than 10%). After three half-lives (3 years), the activity decreases to 12.5%, which is still above 10%. Finally, after four half-lives (4 years), the activity drops to 6.25%, which is indeed less than 10%. Therefore, it takes four years for the radioisotope's activity to drop below 10%. This calculation illustrates the exponential decay of radioisotopes, where each subsequent half-life further reduces the remaining activity by half, demonstrating the significance of understanding half-life in the context of radioactive decay.