Question

Between the years of 1947 and 1956, earthenware jars containing what are known as the Dead Sea Scrolls were found in caves along the coast of Jerusalem in the Dead Sea. Upon radiometric testing, it was found that the scrolls were wrapped in material that contained about 79 percent of the original carbon-14. Archeologists estimated that the scrolls are about 1,900 years old. Are they right?

1. Using the half-life of carbon-14 (5,730 years), prove or disprove this estimate age. Describe how you are testing this hypothesis.

2. What percent of carbon-14 will be left after another 5,000 years?

Answer 1

Carbon-14 dating can be used to estimate the age of the Dead Sea Scrolls. By comparing the amount of carbon-14 in the scrolls with the amount in living organisms, archaeologists can estimate the age of the scrolls. The estimated age of 1,900 years for the scrolls contradicts the amount of carbon-14 remaining.

Step-by-step explanation:

Carbon-14 dating can be used to estimate the age of the Dead Sea Scrolls by measuring the amount of carbon-14 remaining in the material they were wrapped in. The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, the amount of carbon-14 in a sample decreases by half. By comparing the amount of carbon-14 in the scrolls with the amount in living organisms, archaeologists can estimate the age of the scrolls.

To test the hypothesis that the Dead Sea Scrolls are about 1,900 years old, we can use the half-life of carbon-14 to calculate the expected amount of carbon-14 remaining after 1,900 years. We know that after one half-life, 50% of the carbon-14 will remain, so after 2 half-lives (11,460 years), 25% will remain, and after 3 half-lives (17,190 years), 12.5% will remain. Therefore, after 1,900 years, we can expect the scrolls to have less than 12.5% of the original carbon-14, which contradicts the estimated age of 1,900 years.

To calculate the percent of carbon-14 that will be left after another 5,000 years, we can use the same method. After one half-life (5,730 years), 50% will remain, so after two half-lives (11,460 years), 25% will remain. Therefore, after 5,000 years, we can expect the remaining carbon-14 to be less than 25%.