College

One of the radioactive isotopes used in medical treatment or analysis is palladium-103. The half-life of palladium-103 is 17 days. How many days are required for the activity of a sample of palladium-103 to fall to 12.5 percent of its original value?

Answer :

Sure! Let's break down the problem step by step to find out how many days it takes for the activity of a sample of palladium-103 to decrease to 12.5% of its original value.

1. Understand the Half-Life Concept:
- The half-life of a substance is the time it takes for half of its atoms to decay or reduce in activity. For palladium-103, the half-life is 17 days.

2. Initial Activity Level:
- We start with an activity level of 100%.

3. Successive Half-Lives:
- After the first half-life (17 days), the remaining activity is 50% of the original.
- After the second half-life (another 17 days, totaling 34 days), the activity decreases to 25% of the original.
- After the third half-life (a further 17 days, now totaling 51 days), the activity reduces to 12.5% of the original value.

4. Number of Half-Lives Required:
- To reduce the activity to 12.5%, it takes exactly three half-lives.

5. Final Calculation:
- Since each half-life is 17 days, the total time required is [tex]\(3 \times 17\)[/tex] days.
- This equals 51 days.

So, it will take 51 days for the activity of a sample of palladium-103 to fall to 12.5% of its original value.