Each time you dumped the pennies, one half-life passed; it has been shown that the half-life for this radioactive isotope is 20 years. In the year 2000, an archaeology team unearths pottery and is using this isotope for radiometric dating to place the age of the pottery. It is shown that 95% of the nuclei have decayed. Using your graph, approximately how long ago was the pottery made?

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
icon
Concept explainers
Question

Each time you dumped the pennies, one half-life passed; it has been shown that the
half-life for this radioactive isotope is 20 years. In the year 2000, an archaeology team
unearths pottery and is using this isotope for radiometric dating to place the age of the
pottery. It is shown that 95% of the nuclei have decayed. Using your graph,
approximately how long ago was the pottery made?

## Understanding Radioactive Decay: Half-Life and Remaining Nuclei

### Graph: Remaining Nuclei as a Function of Half-Life

This graph represents the relationship between the mass of remaining nuclei and the number of half-lives that have elapsed. The x-axis denotes the number of half-lives, labeled as "Half-life (integer)," ranging from 0 to 6. The y-axis indicates the "Mass of Remaining Nuclei (grams)," ranging from 0 to 0.9 grams.

#### Key Observations:

1. **Decay Curve**: The graph shows a decaying exponential curve, indicating that as the number of half-lives increases, the mass of remaining nuclei decreases.
2. **Initial Mass**: At 0 half-lives, the initial mass of the nuclei is at its peak of approximately 0.9 grams.
3. **Decay Stages**:
    - By the end of the 1st half-life, the mass of remaining nuclei decreases to about 0.45 grams.
    - By the end of the 2nd half-life, the mass further decreases to around 0.225 grams.
    - As more half-lives elapse, the mass of remaining nuclei continues to fall, approaching close to zero by the 5th to 6th half-life.

#### Educational Insight:
This graph highlights a fundamental concept in radioactive decay. Key terms include:
- **Half-Life**: The amount of time it takes for half of the radioactive nuclei in a sample to decay.
- **Exponential Decay**: The process where the quantity decreases by a consistent percentage over equal time periods.

In practical terms, this decay behavior is crucial in fields such as radiometric dating, nuclear medicine, and understanding the stability of radioactive elements. This graph aids in visualizing how quickly a substance can decay, reinforcing the nature of exponential decay in radioactive materials.
Transcribed Image Text:## Understanding Radioactive Decay: Half-Life and Remaining Nuclei ### Graph: Remaining Nuclei as a Function of Half-Life This graph represents the relationship between the mass of remaining nuclei and the number of half-lives that have elapsed. The x-axis denotes the number of half-lives, labeled as "Half-life (integer)," ranging from 0 to 6. The y-axis indicates the "Mass of Remaining Nuclei (grams)," ranging from 0 to 0.9 grams. #### Key Observations: 1. **Decay Curve**: The graph shows a decaying exponential curve, indicating that as the number of half-lives increases, the mass of remaining nuclei decreases. 2. **Initial Mass**: At 0 half-lives, the initial mass of the nuclei is at its peak of approximately 0.9 grams. 3. **Decay Stages**: - By the end of the 1st half-life, the mass of remaining nuclei decreases to about 0.45 grams. - By the end of the 2nd half-life, the mass further decreases to around 0.225 grams. - As more half-lives elapse, the mass of remaining nuclei continues to fall, approaching close to zero by the 5th to 6th half-life. #### Educational Insight: This graph highlights a fundamental concept in radioactive decay. Key terms include: - **Half-Life**: The amount of time it takes for half of the radioactive nuclei in a sample to decay. - **Exponential Decay**: The process where the quantity decreases by a consistent percentage over equal time periods. In practical terms, this decay behavior is crucial in fields such as radiometric dating, nuclear medicine, and understanding the stability of radioactive elements. This graph aids in visualizing how quickly a substance can decay, reinforcing the nature of exponential decay in radioactive materials.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 12 images

Blurred answer
Knowledge Booster
Radioactive decay
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON