Pretend you find a rock with 3.125% parent atoms and 96.875% daughter atoms. How many half-lives have passed?
Understand the Problem
The question asks how many half-lives have passed based on the given percentages of parent and daughter atoms in a rock sample. Since 3.125% of the original parent atoms remain, we need to calculate the number of half-lives it takes for the parent atoms to decay from 100% to 3.125%. Each half-life halves the amount of parent atoms.
Answer
5
Answer for screen readers
5
Steps to Solve
- Understand Half-Life Concept
Half-life is the time taken for half of the parent atoms to decay. To find out how many half-lives have passed, we start from 100% and see how many halvings it takes to reach 3.125%.
- Calculate Remaining Parent Atoms After Each Half-Life
Starting from 100%:
- After 1 half-life: $100% \div 2 = 50%$ remaining
- After 2 half-lives: $50% \div 2 = 25%$ remaining
- After 3 half-lives: $25% \div 2 = 12.5%$ remaining
- After 4 half-lives: $12.5% \div 2 = 6.25%$ remaining
- After 5 half-lives: $6.25% \div 2 = 3.125%$ remaining
- Determine the Number of Half-Lives
From the calculations, we see that it takes 5 half-lives to reduce 100% parent atoms to 3.125%.
5
More Information
The calculation shows that after 5 half-lives, the remaining amount of parent atoms reaches exactly 3.125%. This demonstrates the exponential decay characteristic of radioactive isotopes such as Carbon-14.
Tips
- Misunderstanding half-lives: Some may not realize that each half-life halves the amount, leading to wrong counts.
- Skipping steps: Not calculating the percentages after each half-life can confuse the progression of decay.
AI-generated content may contain errors. Please verify critical information
