Use the following half-life graph to answer the question: Mass Remaining (mg) 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0.0 Half-Life Graph of a Radioactive Isotope 1.0 2.0 What is the half-life of the isotope? 3.0 Time (minutes) 4.0 5.0 6.0
Use the following half-life graph to answer the question: Mass Remaining (mg) 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0.0 Half-Life Graph of a Radioactive Isotope 1.0 2.0 What is the half-life of the isotope? 3.0 Time (minutes) 4.0 5.0 6.0
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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![This image displays a list of labels paired with their corresponding time values. The information is presented as follows:
- Label "a" is associated with a time of 1.0 minutes.
- Label "b" is associated with a time of 3.0 minutes.
- Label "c" is associated with a time of 5.0 minutes.
- Label "d" is associated with a time of 6.0 minutes.
No graphs or diagrams are present in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04eb1b50-f8d1-478c-aaa5-5987cc7d1a2e%2F419b8aa2-268e-41be-b05b-543479a8534e%2Fagwkf2s_processed.png&w=3840&q=75)
Transcribed Image Text:This image displays a list of labels paired with their corresponding time values. The information is presented as follows:
- Label "a" is associated with a time of 1.0 minutes.
- Label "b" is associated with a time of 3.0 minutes.
- Label "c" is associated with a time of 5.0 minutes.
- Label "d" is associated with a time of 6.0 minutes.
No graphs or diagrams are present in the image.
![---
### Understanding Half-Life: Graph Analysis
Use the following half-life graph to answer the question:
#### Half-Life Graph of a Radioactive Isotope
A graph is presented that shows the decay of a radioactive isotope over time. The x-axis represents the time in minutes, ranging from 0.0 to 6.0 minutes, while the y-axis measures the mass remaining in milligrams (mg), with values from 0.0 to 60.0 mg.
- At time 0.0 minutes, the mass remaining is 60.0 mg.
- At time 1.0 minute, the mass has decreased to approximately 30.0 mg.
- At time 2.0 minutes, the mass is about 15.0 mg.
- By 3.0 minutes, the mass is approximately 7.5 mg.
- At 4.0 minutes, the mass remaining is roughly 4.0 mg.
- By 5.0 minutes, the mass is close to 2.0 mg.
The graph exhibits an exponential decay pattern, which is characteristic of radioactive isotope decay.
### Question
**What is the half-life of the isotope?**
To determine the half-life, we observe the time it takes for the mass of the isotope to reduce to half of its initial value:
- Initial mass at 0.0 minutes: 60.0 mg
- Mass at 1.0 minute: 30.0 mg
From the graph, it is evident that the half-life of the isotope is **1.0 minute**, as it takes this amount of time for the mass of the isotope to decrease from 60.0 mg to 30.0 mg.
---
This explanation and interpretation should aid in understanding how to read a half-life graph and determine the half-life of a radioactive isotope.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04eb1b50-f8d1-478c-aaa5-5987cc7d1a2e%2F419b8aa2-268e-41be-b05b-543479a8534e%2Fsz30vw_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Understanding Half-Life: Graph Analysis
Use the following half-life graph to answer the question:
#### Half-Life Graph of a Radioactive Isotope
A graph is presented that shows the decay of a radioactive isotope over time. The x-axis represents the time in minutes, ranging from 0.0 to 6.0 minutes, while the y-axis measures the mass remaining in milligrams (mg), with values from 0.0 to 60.0 mg.
- At time 0.0 minutes, the mass remaining is 60.0 mg.
- At time 1.0 minute, the mass has decreased to approximately 30.0 mg.
- At time 2.0 minutes, the mass is about 15.0 mg.
- By 3.0 minutes, the mass is approximately 7.5 mg.
- At 4.0 minutes, the mass remaining is roughly 4.0 mg.
- By 5.0 minutes, the mass is close to 2.0 mg.
The graph exhibits an exponential decay pattern, which is characteristic of radioactive isotope decay.
### Question
**What is the half-life of the isotope?**
To determine the half-life, we observe the time it takes for the mass of the isotope to reduce to half of its initial value:
- Initial mass at 0.0 minutes: 60.0 mg
- Mass at 1.0 minute: 30.0 mg
From the graph, it is evident that the half-life of the isotope is **1.0 minute**, as it takes this amount of time for the mass of the isotope to decrease from 60.0 mg to 30.0 mg.
---
This explanation and interpretation should aid in understanding how to read a half-life graph and determine the half-life of a radioactive isotope.
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