Question

How old is something if it contains 3.125 of the parent isotope?

A) One half-life
B) Two half-lives
C) Three half-lives
D) Four half-lives

Answer 1

If a sample contains 3.125% of the parent isotope, it indicates that the sample has undergone five half-lives, as each half-life reduces the amount of the substance by half.

Step-by-step explanation:

If a sample contains 3.125% of the parent isotope, then it has undergone five half-lives. One way to understand this is to consider that with each half-life, the amount of the original isotope is reduced by half. Let's see the breakdown:

1. After the first half-life, 50% of the isotope remains.
2. After the second half-life, 25% (or 50% of the previous 50%) remains.
3. After the third half-life, 12.5% (or 50% of the previous 25%) remains.
4. After the fourth half-life, 6.25% (or 50% of the previous 12.5%) remains.
5. Finally, after the fifth half-life, 3.125% (or 50% of the previous 6.25%) remains.

Therefore, the correct answer would actually be five half-lives which is not listed among the provided options A) One half-life B) Two half-lives C) Three half-lives D) Four half-lives.