Biology: Concepts and Investigations
Biology: Concepts and Investigations
3rd Edition
ISBN: 9780073525549
Author: Mariëlle Hoefnagels Dr.
Publisher: McGraw-Hill Education
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Chapter 13, Problem 1MCQ

You discover that a 24,000-year-old fossil has one fourth the concentration of a radioactive isotope compared to a living organism.

What is the half-life of this isotope?

  1. a. 3000 years
  2. b. 6000 years
  3. c. 8000 years
  4. d. 12,000 years
Expert Solution & Answer
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Summary Introduction

Introduction:

The radioactive isotopes are used for the determining the age of fossils. The half-life of the radioactive isotope is used and the age of the fossil is calculated. The technique of using radioactive isotopes in determining the age of fossils is called radioactive dating.

Answer to Problem 1MCQ

Correct answer:

The half-life of the isotope is 12,000 years. Therefore, option d. is correct.

Explanation of Solution

Reason for the correct statement:

The formula for the calculation of the half-life of an isotope where A is the remaining amount of the radioactive isotope, Ao is the initial amount of radioactive isotope, it is the age of the fossil, and T is the half-life of the isotope is as follows:

A = A× (12)t/T

Here, the concentration of the radioactive isotope is one-fourth that of the original matter. So, the A is equal to one fourth of Ao . The age of the fossil is 24,000 years.

A = 14At= 24,000 years

A = A× (12)t/T 14A= A× (12)24,000/T14=(12)24,000/T(12)2=(12)24,000/T

(12)2=(12)24,000/T2 = 24,000T T = 24,0002T = 12,000

Option d. is given as “ 12,000 years”.

As, “the half-life for the radioactive isotope is 12,000 years, which is present in fossil whose age is 24,000 years and the concentration of the radioactive isotope is 14 that of the living organism”, is the right answer.

Hence, the option d. is correct.

Reasons for the incorrect statements:

Option a. is given as “ 3000 years”.

The half-life of the radioactive isotope will be 3000 years when the age of the fossil is 24,000 years and the concentration of the radioactive isotope is 1256 that of the living organism. So, it is a wrong answer.

Option b. is given as “ 6000 years”.

The half-life of the radioactive isotope will be 6000 years when the age of the fossil is 24,000 years and the concentration of the radioactive isotope is 116 that of the living organism. So, it is a wrong answer.

Option c. is given as “ 8000 years”.

The half-life of the radioactive isotope will be 8000 years when the age of the fossil is 24,000 years and the concentration of the radioactive isotope is 18 that of the living organism. So, it is a wrong answer.

Hence, options a., b., and c. are incorrect.

Conclusion

The half-life for the radioactive isotope is 12,000 years, which is present in fossil whose age is 24,000 years and the concentration of the radioactive isotope is 14 that of the living organism.

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Chapter 13 Solutions

Biology: Concepts and Investigations

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