A radioactive sample decays with a half-life of 71.19 minutes. If the original activity of the sample was 16.352 mCi, what is the activity of the sample after 2.548 hours have passed? Express your answer in terms of mCi using at least three significant figures.
A radioactive sample decays with a half-life of 71.19 minutes. If the original activity of the sample was 16.352 mCi, what is the activity of the sample after 2.548 hours have passed? Express your answer in terms of mCi using at least three significant figures.
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
![**Problem Statement:**
A radioactive sample decays with a half-life of 71.19 minutes. If the original activity of the sample was 16.352 mCi, what is the activity of the sample after 2.548 hours have passed?
Express your answer in terms of mCi using at least three significant figures.
**Solution Template:**
- Calculate total elapsed time in minutes: \[ \text{Elapsed time} = 2.548 \, \text{hours} \times 60 \, \text{minutes/hour} \]
- Total elapsed time: \[ 2.548 \times 60 = 152.88 \, \text{minutes} \]
- Use the decay formula: \[ A(t) = A_0 \times \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}} \]
- Where:
- \( A(t) \) = Activity at time \( t \)
- \( A_0 \) = Original activity (16.352 mCi)
- \( t \) = Elapsed time (152.88 minutes)
- \( T_{1/2} \) = Half-life of the sample (71.19 minutes)
- Substitute the values:
\[ A(152.88) = 16.352 \times \left( \frac{1}{2} \right)^{\frac{152.88}{71.19}} \]
- Calculate:
\[ A(152.88) = 16.352 \times \left( \frac{1}{2} \right)^{2.148} \]
- Using values from the calculation:
\[ \left( \frac{1}{2} \right)^{2.148} \approx 0.221 \]
- Therefore:
\[ A(152.88) \approx 16.352 \times 0.221 \approx 3.614 \, \text{mCi} \]
Final Answer:
\[ \approx 3.614 \, \text{mCi} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F703b43e5-ae23-420c-b3a8-d626b9b6023e%2F34f780f0-e166-4948-9f51-d2fdebe9e2c7%2Fc4hdk2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A radioactive sample decays with a half-life of 71.19 minutes. If the original activity of the sample was 16.352 mCi, what is the activity of the sample after 2.548 hours have passed?
Express your answer in terms of mCi using at least three significant figures.
**Solution Template:**
- Calculate total elapsed time in minutes: \[ \text{Elapsed time} = 2.548 \, \text{hours} \times 60 \, \text{minutes/hour} \]
- Total elapsed time: \[ 2.548 \times 60 = 152.88 \, \text{minutes} \]
- Use the decay formula: \[ A(t) = A_0 \times \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}} \]
- Where:
- \( A(t) \) = Activity at time \( t \)
- \( A_0 \) = Original activity (16.352 mCi)
- \( t \) = Elapsed time (152.88 minutes)
- \( T_{1/2} \) = Half-life of the sample (71.19 minutes)
- Substitute the values:
\[ A(152.88) = 16.352 \times \left( \frac{1}{2} \right)^{\frac{152.88}{71.19}} \]
- Calculate:
\[ A(152.88) = 16.352 \times \left( \frac{1}{2} \right)^{2.148} \]
- Using values from the calculation:
\[ \left( \frac{1}{2} \right)^{2.148} \approx 0.221 \]
- Therefore:
\[ A(152.88) \approx 16.352 \times 0.221 \approx 3.614 \, \text{mCi} \]
Final Answer:
\[ \approx 3.614 \, \text{mCi} \]
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 3 steps with 3 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