The half-life of carbon 14 is 5730 years. If a 1-gram sample of old carbon is 1/8 as radioactive as 1-gram of a current sample, then the age of the old sample is about

Question

Quizplus · Accepted Answer

The ratio of radioactive carbon in the old sample to that in the current sample is 1/8. This means that 1/8 of the radioactive carbon has decayed. Using the concept of half-life, we know that after one half-life, the amount of radioactive carbon remaining is half of the original amount. Therefore, after one half-life, 1/2 of the radioactive carbon in the old sample will remain, which is equal to 1/8 of the radioactive carbon in the current sample. This implies that the old sample is 1 half-life old, or 5730 years old. Continuing this logic, we can see that 2 half-lives have passed, which means the old sample is 2 x 5730 = 11,460 years old, which is closest to choice C) 17,200 years.

The Half-Life of Carbon 14 Is 5730 Years