So I have this word problem and I’m a bit confused about it. I have the answer and explanation but I still don’t understand:
The half-life of carbon-14 is approximately 5730 years, while the half-life of carbon-12 is essentially infinite. If the ratio of carbon-14 to carbon-12 in a certain sample is 25% less than the normal ratio in nature, how old is the sample?
A. Less than 5730 years B. Approximately 5730 years C. Significantly greater than 5730 years, but less than 11460 years D. Approximately 11460 years
Correct Answer: A
Because the half-life of carbon-12 is essentially infinite, a 25 percent decrease in the ratio of carbon-14 to carbon-12 means the same as a 25 percent decrease in the amount of carbon-14. If less than half of the carbon-14 has deteriorated, then less than one half-life has elapsed. Therefore, the sample is less than 5730 years old. Be careful with the wording here—the question states that the ratio is 25% less than the ratio in nature, not 25% of the ratio in nature, which would correspond to choice (D).
How is the ratio of the carbon isotopes relevant to half-lives? What is the purpose of saying the half-life of an isotope is infinite? What is meant by “the normal ratio in nature”? Just based on the answer, it seems like the question said “25% of a carbon sample decayed, how old is this sample?” Obviously it’s younger than 5,730 years (the time for its first half life) because if only 25% decayed that means half a half-life has passed. I don’t see how isotopes and ratios would change this problem at all.
Edit: Every answer here was very informative and helpful. It was tough to pick a best answer. I picked Cosma’s because it clicked with me.
If you’re reading this and want to understand radiocarbon dating, look at every answer because there is some useful information in every answer