Question

The radionuclide carbon-14 is a beta emitter used to date archeological

and historical artifacts containing organic matter. It has a half-life of 5730
years. How many years must pass for an original 1,250 picogram sample
of carbon-14 to decay to 9.76 picograms?
40,110 years
34,380
45,840 years
28,650 years

Answer 1

To determine the number of years required for a sample of carbon-14 to decay, we can use the concept of half-life. The half-life of carbon-14 is 5730 years. By dividing the initial amount by the final amount and taking the logarithm base 2, we can find the number of half-lives. Multiplying the number of half-lives by the half-life period will give us the number of years required.

Step-by-step explanation:

Carbon-14 is a radioactive isotope with a half-life of 5730 years. To determine how many years are required for an original 1,250 picogram sample of carbon-14 to decay to 9.76 picograms, we can use the concept of half-life. Since the half-life of carbon-14 is 5730 years, we can calculate the number of half-lives it takes for the sample to decay to the given amount. By dividing the initial amount by the final amount and taking the logarithm base 2, we can find the number of half-lives. Multiplying the number of half-lives by the half-life period will give us the number of years required.