Determine the average `.^(14)C` activity in decays per minute per gram of natural carbon found in living organisms if the concentration of `.^(14)C` relative to that of `.^(12)C` is `1.4 xx10^(-12)` and half -life of `.^(14)C` is `T_(1//2)=57.30` years.

Explanation

To determine the average activity of \(^{14}C\) in decays per minute per gram of natural carbon found in living organisms, we will follow these steps:

### Step 1: Calculate the decay constant (\(\lambda\))
The decay constant is given by the formula:
\[ \lambda = \frac{\ln(2)}{T_{1/2}} \]
where \(T_{1/2} = 57.30\) years. First, we need to convert the half-life into minutes:
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