Question

Ash from an early pit was found to be 0.390% as much carbon-14 as found in a similar sample of ash today. The half-life of C-14 is 5,730 years. How old is this early pot ash?

a. 2,865 yrs
b. 17,190 yrs
c. 45,840 yrs
d. 11,460 yrs
e. 40,110 yrs

Answer 1

The age of the early pot ash, calculated using the carbon-14 dating method, is approximately 45,840 years. This is based on the number of half-lives passed to reach the current percentage of C-14 found in the sample.

Step-by-step explanation:

To calculate the age of the early pot ash based on the carbon-14 (C-14) dating method, we can use the half-life formula. Since the ash contains 0.390% of the carbon-14 found in a similar sample today, we need to determine how many half-lives have passed to reach this percentage. The half-life of C-14 is 5,730 years.

Starting with 100% of C-14, one half-life reduces the amount to 50%, the second to 25%, the third to 12.5%, and so on. The formula used for this calculation is the percentage of C-14 remaining = (1/2)^(n), where 'n' is the number of half-lives. We'll have:

0.390% = (1/2)^(n) => n = log(0.0039)/log(0.5) = 8.298 half-lives.

Then we multiply the number of half-lives by the length of one half-life: 8.298 * 5,730 years to find the age of the pot ash. This equals approximately 47,548 years, which isn't an option in the multiple-choice provided. Therefore, based on the answer choices, the closest match to the calculated age is 45,840 years (option c).