In a sample of rock the amount of radioactive carbon is 6.25%. If the half life of radioactive carbon is 5730 years then estimate the age of rock.

Options

A. 11460 years
B. 17190 years
C. 22920 years
D. 28650 years

Answer

To estimate the age of the rock based on the amount of radioactive carbon present, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data**:
- Amount of radioactive carbon remaining = 6.25%
- Half-life of radioactive carbon (C-14) = 5730 years

2. **Determine the Number of Half-Lives**:
- The percentage of radioactive carbon remaining can be expressed in terms of half-lives.
- If we start with 100% of radioactive carbon, after one half-life (5730 years), it would be 50%. After two half-lives, it would be 25%, and after three half-lives, it would be 12.5%. After four half-lives, it would be 6.25%.
- Therefore, the rock has gone through 4 half-lives.

3. **Calculate the Total Age of the Rock**:
- Since each half-life is 5730 years, we can calculate the total age of the rock by multiplying the number of half-lives by the length of one half-life.
- Total age = Number of half-lives × Half-life duration
- Total age = 4 × 5730 years = 22920 years

4. **Final Result**:
- The estimated age of the rock is 22,920 years.