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 \( _{86}^{226}\text{Ra} \) given its half-life and the number of nuclei in the sample, we can follow these steps:

### Step 1: Convert the half-life from years to seconds
The half-life \( T_{1/2} \) is given as \( 1.6 \times 10^3 \) years. To convert this to seconds, we use the following conversion factors:
- 1 year = 365 days
- 1 day = 24 hours
- 1 hour = 3600 seconds

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