The half life for the decay of carbon-14 is 5.73 × 10³ years. Suppose the activity due to the radioactive decay of the carbon-14 in a tiny sample of an artifact made of wood from an archeological dig is measured to be 1.1 × 10³ Bq. The activity in a similar-sized sample of fresh wood is measured to be 1.4× 10³ Bq. Calculate the age of the artifact. Round your answer to 2 significant digits. years ☐ x10 X
The half life for the decay of carbon-14 is 5.73 × 10³ years. Suppose the activity due to the radioactive decay of the carbon-14 in a tiny sample of an artifact made of wood from an archeological dig is measured to be 1.1 × 10³ Bq. The activity in a similar-sized sample of fresh wood is measured to be 1.4× 10³ Bq. Calculate the age of the artifact. Round your answer to 2 significant digits. years ☐ x10 X
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
Related questions
Question
![### Understanding Carbon-14 Dating
**The Problem:**
The half-life for the decay of carbon-14 is \(5.73 \times 10^3\) years.
Suppose the activity due to the radioactive decay of the carbon-14 in a tiny sample of an artifact made of wood from an archeological dig is measured to be \(1.1 \times 10^3\) Bq. The activity in a similar-sized sample of fresh wood is measured to be \(1.4 \times 10^3\) Bq. Calculate the age of the artifact. Round your answer to 2 significant digits.
\[ \text{Box for input: } [ \text{years} ] \]
**Detailed Explanation:**
The question involves determining the age of an artifact using carbon-14 dating. This technique is based on the principle of radioactive decay, where the half-life of carbon-14 is used to estimate the time since the death of an organism (in this case, the wood used to create the artifact).
To solve this, you can use the formula for radioactive decay:
\[ N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} \]
Where:
- \( N \) is the current activity (1.1 x 10\(^3\) Bq).
- \( N_0 \) is the initial activity (1.4 x 10\(^3\) Bq).
- \( t \) is the time elapsed since the death of the organism.
- \( t_{1/2} \) is the half-life of carbon-14 (5.73 x 10\(^3\) years).
**Steps:**
1. Determine the ratio of activities: \( \frac{N}{N_0} = \frac{1.1 \times 10^3}{1.4 \times 10^3} \).
2. Calculate \( t \) using the formula above.
This method helps archaeologists estimate the age of artifacts and contributes significantly to our understanding of ancient civilizations and historical timelines.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89b126cf-58b3-49ad-9704-387f30e63dfe%2F950a21e8-656d-4301-86dd-9790a8b7955f%2Fhdp20on_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Carbon-14 Dating
**The Problem:**
The half-life for the decay of carbon-14 is \(5.73 \times 10^3\) years.
Suppose the activity due to the radioactive decay of the carbon-14 in a tiny sample of an artifact made of wood from an archeological dig is measured to be \(1.1 \times 10^3\) Bq. The activity in a similar-sized sample of fresh wood is measured to be \(1.4 \times 10^3\) Bq. Calculate the age of the artifact. Round your answer to 2 significant digits.
\[ \text{Box for input: } [ \text{years} ] \]
**Detailed Explanation:**
The question involves determining the age of an artifact using carbon-14 dating. This technique is based on the principle of radioactive decay, where the half-life of carbon-14 is used to estimate the time since the death of an organism (in this case, the wood used to create the artifact).
To solve this, you can use the formula for radioactive decay:
\[ N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} \]
Where:
- \( N \) is the current activity (1.1 x 10\(^3\) Bq).
- \( N_0 \) is the initial activity (1.4 x 10\(^3\) Bq).
- \( t \) is the time elapsed since the death of the organism.
- \( t_{1/2} \) is the half-life of carbon-14 (5.73 x 10\(^3\) years).
**Steps:**
1. Determine the ratio of activities: \( \frac{N}{N_0} = \frac{1.1 \times 10^3}{1.4 \times 10^3} \).
2. Calculate \( t \) using the formula above.
This method helps archaeologists estimate the age of artifacts and contributes significantly to our understanding of ancient civilizations and historical timelines.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY