`C^(14)` has a half life of 5700 yrs. At the end of 11400 years, the actual amount left is

Options

A. 0.5 of original amount
B. 0.25 of original amount
C. 0.125 of original amount
D. 0.0625 of original amount

Explanation

To solve the problem of how much Carbon-14 (C-14) is left after 11,400 years, given its half-life of 5,700 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Half-life of C-14, \( t_{1/2} = 5700 \) years
- Total time elapsed, \( t = 11400 \) years

2. **Calculate the Number of Half-Lives:**
- The number of half-lives \( n \) can be calculated using the formula:
\[ n = \frac{t}{t_{1/2}} \]
- Substituting the values:
\[ n = \frac{11400}{5700} = 2 \]

3. **Determine the Remaining Amount:**
- The remaining amount of a substance after \( n \) half-lives can be calculated using the formula:
\[ N = N_0 \left(\frac{1}{2}\right)^n \]
- Here, \( N_0 \) is the original amount, and \( N \) is the amount remaining after \( n \) half-lives.
- Substituting \( n = 2 \):
\[ N = N_0 \left(\frac{1}{2}\right)^2 = N_0 \cdot \frac{1}{4} \]

4. **Conclusion:**
- Therefore, after 11,400 years, the amount of C-14 left is \( 0.25 \) times the original amount \( N_0 \).

### Final Answer:
The actual amount left after 11,400 years is **0.25 of the original amount**.

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