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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.
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.
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