Question

The half-life of carbon-14 is about 6000 years. Assume that a sample of charcoal was formed by burning of living wood about 12,000 years ago. How much of the original carbon-14 would remain in the wood today?

1) all of it
2) one half
3) one fourth
4) one eighth
5) one sixteenth

Answer 1

After 12,000 years, or two half-lives of carbon-14, one fourth of the original C-14 would remain in the wood today. This remaining fraction is used in the process of radiocarbon dating to estimate the age of formerly living material.

Step-by-step explanation:

If a sample of charcoal formed by the burning of living wood was created about 12,000 years ago, and given that the half-life of carbon-14 (C-14) is about 6000 years, we would expect that after one half-life (6000 years), half of the original C-14 would remain in the sample, and after two half-lives (12,000 years), one fourth of the original C-14 would be left. To put it mathematically, the amount of C-14 remaining after 'n' number of half-lives can be calculated using the formula (1/2)^n, where 'n' is the number of half-lives. Since 12,000 years is equal to two half-lives of C-14 (6000 years each), we apply this formula: (1/2)^2 = 1/4.

So, the correct answer would be one fourth of the original carbon-14 would remain in the wood today. This principle is used in the technique of radiocarbon dating which relies on measuring the remaining C-14 in formerly living material to estimate its age. More specifically, radiocarbon dating measures the ratio of carbon-14 to carbon-12 (C-12), since C-12 remains constant whereas C-14 decreases over time following the death of the organism.