Chapter 14, Problem 4A

Summary Introduction

Introduction:

A fossil is any preserved evidence of an organism. Radiometric dating is used to measure the age of a rock. It uses the decay of radioactive isotopes to measure the age of a rock. The method requires that the half-life of the isotope is known. The relative amounts of a radioactive isotope and its decay product must also be known.

Answer to Problem 4A

Correct answer:

The correct answer is option C. 11,460 years old

Explanation of Solution

Explanation/justification for the correct answer:

Option C. 11,460 years old −According to the given data carbon- 14 has a half-life of 5730 years. It is given that one- fourth of the original radioactive carbon is present in the fossil.

So after 5730 years half of the original radioactive carbon is present in the fossil. After another 5730 years, one- fourth of the original radioactive carbon will be present in the fossil.

Hence age of the fossil= 5730 + 5730= 11, 460 years.

Hence this is the correct option.

Explanation for incorrect answer:

Option A. 2857.5 years old- According to the given data carbon- 14 has a half-life of 5730 years and one-fourth of the original radioactive carbon is present in the fossil.

The age of the fossil cannot be less than the half-life of carbon.

Hence this is not the correct option.

Option B. 5730 years old- According to the given data carbon- 14 has a half-life of 5730 years and one-fourth of the original radioactive carbon is present in the fossil.

After 5730 years half of the original radioactive carbon will be present in the fossil. So the age of the fossil has to be more than the half-life of carbon as one- fourth of the original radioactive carbon is present in the fossil.

Hence this is not the correct option.

Option D. 17,145 years old− According to the given data carbon- 14 has a half-life of 5730 years and one-fourth of the original radioactive carbon is present in the fossil.

So after 5730 years half of the original radioactive carbon is present in the fossil. After another 5730 years, one- fourth of the original radioactive carbon will be present in the fossil.

Hence, age of fossil= 5730 + 5730= 11, 460 years.

Hence, this is not the correct option.