The radioactivity due to `C-14` isotope (half-life = 6000 years) of a sample of wood form an ancient tomb was found to be nearly half that of fresh wood. The bomb is there for about

Options

A. 3000 year old
B. 6000 year old
C. 9000 year old
D. 12000 year old

Answer

To solve the problem regarding the radioactivity of the C-14 isotope in the ancient wood sample, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Half-Life Concept**:
The half-life of a radioactive isotope is the time required for half of the radioactive atoms in a sample to decay. For C-14, the half-life is given as 6000 years.

2. **Identify the Initial and Final Amounts**:
The problem states that the radioactivity of the wood sample is nearly half that of fresh wood. This means that the remaining amount of C-14 (N_t) is half of the original amount (N_0):
\[ N_t = \frac{N_0}{2} \]

3. **Use the Half-Life to Determine Time**:
Since the amount of C-14 has decreased to half, we can directly relate this to the half-life. If the amount is half, it indicates that one half-life has passed:
\[ t = \text{half-life} = 6000 \text{ years} \]

4. **Conclusion**:
Therefore, the tomb has been there for approximately 6000 years.

### Final Answer:
The tomb is about **6000 years old**.

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