The half-life period of `C^(14)` is 5760 years. A piece of woods when buried in the earth had `1% C^(14)`. Now as charcoal it has only `0.25% C^(14)`. How long has the piece of wood been buried?

Explanation

To determine how long the piece of wood has been buried, we can use the concept of half-life and the decay of carbon-14. Here’s a step-by-step solution:

### Step 1: Understand the given data
- The half-life of carbon-14 (C-14) is given as \( T_{1/2} = 5760 \) years.
- The initial percentage of C-14 in the wood when buried is \( N_0 = 1\% \).
- The current percentage of C-14 in the charcoal is \( N = 0.25\% \).

### Step 2: Calculate the decay constant (k)
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