Given the half-life of carbon-14 is approximately 5,700 years, how long will it take for a 50 gram sample to decay to 6.25 grams?

To determine how long it will take for a 50 gram sample of carbon-14 to decay to 6.25 grams, it's essential to understand the concept of half-lives. The half-life of a substance is the time it takes for half of the initial quantity to decay.

Starting with the initial amount of carbon-14:

1. After one half-life (5,700 years), the amount decays to half of 50 grams, which is 25 grams.

2. After two half-lives (11,400 years), the amount decays to half of 25 grams, resulting in 12.5 grams.

3. After three half-lives (17,100 years), the amount decays to half of 12.5 grams, resulting in 6.25 grams.

Thus, it takes three half-lives for the original 50 grams to decay to 6.25 grams, and since each half-life is 5,700 years, the total time is:

3 half-lives * 5,700 years/half-life = 17,100 years.

This calculation shows that the correct answer is indeed 17,100 years.