What is the minimum half-life of an isotope needed so that not more than 0.1% of the nuclei undergo decay during a 3-hour laboratory period?

Explanation

To find the minimum half-life of an isotope needed so that not more than 0.1% of the nuclei undergo decay during a 3-hour laboratory period, we can follow these steps:

### Step 1: Understand the Problem
We need to ensure that after 3 hours, no more than 0.1% of the initial quantity of the isotope has decayed. This means that at least 99.9% of the isotope must remain.

### Step 2: Set Up Initial Conditions
Let the initial quantity of the isotope be \( N_0 = 100 \). After 3 hours, we want the remaining quantity \( N \) to be:
\[
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