Question

A rock with only 25% of the parent isotope left has been decaying for time equal to ______ half-lives.

Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4

Answer 1

A rock with only 25% of the parent isotope left has been decaying for a time equal to 3. 3 half-lives.

Step-by-step explanation:

A rock with only 25% of the parent isotope left has been decaying for a time equal to 3. 3 half-lives. After one half-life, half of the sample is left; after two half-lives, one half of the remainder (or one quarter) is left; and after three half-lives, one half of that (or one eighth) is left.

Let's think step by step:

1. After the first half-life, 50% of the parent isotope remains.
2. After the second half-life, half of the remaining 50% (25%) remains.
3. After the third half-life, half of the remaining 25% (12.5%) remains.

Therefore, it takes

3 half-lives

for the rock to have only 25% of the parent isotope left.