Question

What percentage of 146c (t1/2 = 5715 years) remains in a sample estimated to be 14730 years old?

Answer 1

To find the percentage of C-14 remaining in a 14730-year-old sample, we determine it is 2.57 half-lives old. Applying the half-life formula, we calculate that approximately 9% of the original C-14 is left.

Step-by-step explanation:

The decay of Carbon-14 (C-14) can be modelled using the concept of half-lives. The half-life of C-14 is 5730 years. To determine how much of a C-14 sample remains after a certain period, we apply the formula N = N0(½)^(t/t1/2), where N is the final amount of C-14, N0 is the initial amount of C-14, t is the time elapsed, and t1/2 is the half-life of C-14.

To find out the percentage of C-14 remaining in a sample that is 14730 years old, we first divide the elapsed time by the half-life: 14730 years / 5730 years = 2.57 half-lives. Using the formula, we get N/N0 = (½)2.57, which calculates to approximately 9% of the original C-14 remaining in the sample.

Answer 2

To find the percentage of carbon-14 remaining in a sample estimated to be 14,730 years old, we can use the concept of half-life. With each half-life, the sample decreases to 50% of its original amount. After 2.58 half-lives, the remaining amount would be approximately 12.5% of the original sample.

Step-by-step explanation:

To find the percentage of carbon-14 remaining in a sample estimated to be 14,730 years old, we can use the concept of half-life. Carbon-14 has a half-life of 5,715 years, which means that after each half-life, only half of the sample remains. Since the sample is 14,730 years old, we can calculate the number of half-lives elapsed: 14,730 years / 5,715 years = 2.58 half-lives. With each half-life, the sample decreases to 50% of its original amount, so after 2.58 half-lives, the remaining amount would be: 50% * 50% * 50% * 100% ≈ 12.5% of the original sample.