A 25 g piece of characoal is found in some ruins of an ancient city. The sample shows a `C^(14)` activity of 250 decay/minutes. How long has the three this charcoal came from been dead ? Given, the half-life of `C^(14)` is 5730 years. The ratio of `C^(14) and C^(12)` in the living sample is 1.3 `xx 10^(-12)`.

Explanation

To solve the problem step by step, we will follow the process outlined in the video transcript.

### Step 1: Calculate the Decay Constant (λ)
The decay constant (λ) can be calculated using the formula:
\[ \lambda = \frac{0.693}{t_{1/2}} \]
where \(t_{1/2}\) is the half-life of \(C^{14}\).
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