The half-lives of different radioisotopes are given in the table. Radioisotope Half-life (min) argon-44 12 lead-196 37 potassium-44 22 indium-117 43 If the initial amount of indium-117 is 3.6 g, how much indium-117 is left in the body after 86 min? mass:
The half-lives of different radioisotopes are given in the table. Radioisotope Half-life (min) argon-44 12 lead-196 37 potassium-44 22 indium-117 43 If the initial amount of indium-117 is 3.6 g, how much indium-117 is left in the body after 86 min? mass:
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
![**The Half-Lives of Different Radioisotopes**
The half-lives of different radioisotopes are given in the following table:
| Radioisotope | Half-life (min) |
|----------------|------------------|
| argon-44 | 12 |
| lead-196 | 37 |
| potassium-44 | 22 |
| indium-117 | 43 |
**Problem:**
If the initial amount of indium-117 is 3.6 g, how much indium-117 is left in the body after 86 minutes?
**To solve:**
- First, identify the half-life of indium-117 from the table, which is 43 minutes.
- Determine how many half-lives have passed in 86 minutes.
- Use the formula for radioactive decay to calculate the remaining mass.
\[ \text{Number of half-lives} = \frac{86 \text{ min}}{43 \text{ min/half-life}} = 2 \]
\[ \text{Remaining mass} = \text{Initial mass} \times \left( \frac{1}{2} \right)^n \]
where \( n \) is the number of half-lives.
For two half-lives:
\[ \text{Remaining mass} = 3.6 \text{ g} \times \left( \frac{1}{2} \right)^2 = 3.6 \text{ g} \times \frac{1}{4} = 0.9 \text{ g} \]
Therefore, after 86 minutes, 0.9 grams of indium-117 remains.
**Input box for the educational platform:**
```
mass: ________ g
```
The user is expected to fill in "0.9" in the input box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d591113-c73d-4bf8-a1b7-9966513ce440%2F3d9f4ab6-4062-44ea-afcd-93f9ed64ad46%2Fjh56lwo_processed.png&w=3840&q=75)
Transcribed Image Text:**The Half-Lives of Different Radioisotopes**
The half-lives of different radioisotopes are given in the following table:
| Radioisotope | Half-life (min) |
|----------------|------------------|
| argon-44 | 12 |
| lead-196 | 37 |
| potassium-44 | 22 |
| indium-117 | 43 |
**Problem:**
If the initial amount of indium-117 is 3.6 g, how much indium-117 is left in the body after 86 minutes?
**To solve:**
- First, identify the half-life of indium-117 from the table, which is 43 minutes.
- Determine how many half-lives have passed in 86 minutes.
- Use the formula for radioactive decay to calculate the remaining mass.
\[ \text{Number of half-lives} = \frac{86 \text{ min}}{43 \text{ min/half-life}} = 2 \]
\[ \text{Remaining mass} = \text{Initial mass} \times \left( \frac{1}{2} \right)^n \]
where \( n \) is the number of half-lives.
For two half-lives:
\[ \text{Remaining mass} = 3.6 \text{ g} \times \left( \frac{1}{2} \right)^2 = 3.6 \text{ g} \times \frac{1}{4} = 0.9 \text{ g} \]
Therefore, after 86 minutes, 0.9 grams of indium-117 remains.
**Input box for the educational platform:**
```
mass: ________ g
```
The user is expected to fill in "0.9" in the input box.
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