Final answer:
To determine the age of the ancient fire, we calculate the number of half-lives that have passed with Carbon-14 having a half-life of about 6000 years. As the charcoal has ¼ of the original C-14, this corresponds to two half-lives, indicating the fire occurred approximately 12,000 years ago. option (b) as the correct answer.
Step-by-step explanation:
If charcoal from an ancient fire is analyzed to have only ¼ the C-14 that current carbon on Earth has, we can use the concept of radioactive decay and half-lives to estimate the age of the fire. Since Carbon-14 has a half-life of about 6000 years, one half-life would reduce the amount of C-14 to half. Two half-lives would reduce it to a quarter of the original amount.
Therefore, it takes two half-lives for the C-14 to become ¼ of its original amount. Since one half-life is approximately 6000 years, two half-lives would be 6000 years x 2, which equals 12000 years. So, the fire would have been made approximately 12000 years ago, indicating option (b) as the correct answer.