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1. Review the image attached. How good is our assumption that half of our radioactive “nuclei” decay in each half-life? Explain. 2. If you started with a sample of 600 radioactive nuclei, how many would remain undecayed after three half-lives? 3. If 175 undecayed nuclei remained from a sample of 2800 nuclei, how many half-lives have passed?

1. Review the image attached. How good is our assumption that half of our radioactive “nuclei” decay in each half-life? Explain. 2. If you started with a sample of 600 radioactive nuclei, how many would remain undecayed after three half-lives? 3. If 175 undecayed nuclei remained from a sample of 2800 nuclei, how many half-lives have passed?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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1. Review the image attached. How good is our assumption that half of our radioactive “nuclei” decay in each half-life? Explain.

2. If you started with a sample of 600 radioactive nuclei, how many would remain undecayed after three half-lives?

3. If 175 undecayed nuclei remained from a sample of 2800 nuclei, how many half-lives have passed?
 
4. How many half-lives would it take for 6.02 x 1023 nuclei to decay to 6.25% (0.376 x 1023) of the original number of nuclei?
 
**Understanding Radioactive Decay: Analyzing Half-Lives Through a Bar Graph** This bar graph provides a visual representation of radioactive decay over time measured in half-lives. **Axes Explanation:** - The x-axis represents the number of half-lives, ranging from 0 to 10. - The y-axis indicates the number of undecayed nuclei, ranging from 0 to 12,500. **Graph Description:** - At 0 half-lives, the number of undecayed nuclei is at its maximum, slightly above 12,000. - The number decreases significantly with each subsequent half-life: - At 1 half-life, the number drops to about half, around 6,000. - At 2 half-lives, it reduces further to approximately 3,000. - By 3 half-lives, the number is about 1,500. - The pattern of decrease continues exponentially, with each subsequent bar representing a smaller fraction of undecayed nuclei: - 4 half-lives have less than 1,000 nuclei remaining. - This trend continues until, by 10 half-lives, the number of undecayed nuclei is negligible. **Conclusion:** The graph illustrates the exponential nature of radioactive decay. Each half-life results in the reduction of the undecayed nuclei by about half, demonstrating the predictable mathematical pattern of decay over time. This visualization is crucial in fields like physics and chemistry for understanding the behavior of radioactive materials.
Transcribed Image Text:**Understanding Radioactive Decay: Analyzing Half-Lives Through a Bar Graph** This bar graph provides a visual representation of radioactive decay over time measured in half-lives. **Axes Explanation:** - The x-axis represents the number of half-lives, ranging from 0 to 10. - The y-axis indicates the number of undecayed nuclei, ranging from 0 to 12,500. **Graph Description:** - At 0 half-lives, the number of undecayed nuclei is at its maximum, slightly above 12,000. - The number decreases significantly with each subsequent half-life: - At 1 half-life, the number drops to about half, around 6,000. - At 2 half-lives, it reduces further to approximately 3,000. - By 3 half-lives, the number is about 1,500. - The pattern of decrease continues exponentially, with each subsequent bar representing a smaller fraction of undecayed nuclei: - 4 half-lives have less than 1,000 nuclei remaining. - This trend continues until, by 10 half-lives, the number of undecayed nuclei is negligible. **Conclusion:** The graph illustrates the exponential nature of radioactive decay. Each half-life results in the reduction of the undecayed nuclei by about half, demonstrating the predictable mathematical pattern of decay over time. This visualization is crucial in fields like physics and chemistry for understanding the behavior of radioactive materials.
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