After 5 half-lives, what percentage of the original number of parent atoms is left? _______ (a number)
Question
After 5 half-lives, what percentage of the original number of parent atoms is left?
_______ (a number)
Solution
A half-life is the time it takes for half of the atoms in a sample to decay. After one half-life, 50% of the original atoms remain.
Here's how you calculate the remaining percentage after 5 half-lives:
- After the first half-life, 50% of the original atoms remain.
- After the second half-life, 50% of the remaining 50% (or 25%) of the original atoms remain.
- After the third half-life, 50% of the remaining 25% (or 12.5%) of the original atoms remain.
- After the fourth half-life, 50% of the remaining 12.5% (or 6.25%) of the original atoms remain.
- After the fifth half-life, 50% of the remaining 6.25% (or 3.125%) of the original atoms remain.
So, after 5 half-lives, approximately 3.125% of the original number of parent atoms is left.
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