The half-life of the radioactive nucleus `._(86)^(226)Ra` is `1.6 xx10^(3)yr`. If a sample contains`3.0 xx10^(16)` such nuclei, determine the activity at this time.

Explanation

To determine the activity of the radioactive nucleus \( _{86}^{226}\text{Ra} \) at a given time, we will follow these steps:

### Step 1: Convert Half-Life to Seconds
The half-life \( t_{1/2} \) is given as \( 1.6 \times 10^3 \) years. We need to convert this into seconds.

\[ t_{1/2} = 1.6 \times 10^3 \text{ years} \times 365 \text{ days/year} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]
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