The half-life of a radioactive nucleus is 20 hours. What fraction of original activity will remain after 40 hours?

Explanation

To solve the problem of determining the fraction of original activity that remains after 40 hours given that the half-life of a radioactive nucleus is 20 hours, we can follow these steps:

### Step 1: Understand the Concept of Half-Life
The half-life (t_half) of a radioactive substance is the time required for half of the radioactive nuclei in a sample to decay. After one half-life, 50% of the original activity remains; after two half-lives, 25% remains, and so on.

### Step 2: Identify Given Values
From the problem, we know:
- Half-life (t_half) = 20 hours
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